Mathworks SIMMECHANICS 3 Reference

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SimMechanics™ 3

Reference

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SimMechanics™ Reference

The software described in this document is furnished under a license agreement. The software may be used or copied only under the terms of the license agreement. No part of this manual may be photocopied or reproduced in any form without prior written consent from The MathW orks, Inc.

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Revision History

October 2008 Online only New for Version 3.0 (Release 2008b) March 2009 Online only Revised for Version 3.1 (Release 2009a) September 2009 Online only Revised for Version 3.1.1 (Release 2009b) March 2010 Online only Revised for Version 3.2 (Release 2010a)

Block Reference

Machines, Bodies, and G rounds ..................... 1-2

Contents

Joints

Assembled Joints Disassembled Joints Massless Connectors

Constraints and Drivers

Actuators and Sensors

Force Elements

Interface Elements

Utilities

............................................ 1-2

.................................. 1-2

............................... 1-4

.................................... 1-6

................................ 1-6

........................................... 1-7

............................ 1-5

............................. 1-5

iii

Blocks — Alphabetical List

Function Reference

Configuration Parameters

SimMechanics Pane: General ....................... 4-2

SimMechanics Pane Overview Warn if machine contains redundant constraints Warn if number of initial constraints is unstable Mark automatically cut joints Display machines after updating diagram Show animation during simulation Show only port coordinate systems Default body color (RGB) Default body geometries

....................... 4-3

........ 4-4

........ 4-6

....................... 4-8

............. 4-10

................... 4-12

................... 4-14

........................... 4-16

............................ 4-18

iv Contents

Index

Block Reference

Machines, Bodies, and Grounds (p. 1-2)

Joints (p. 1-2) Add degrees of freedom

Constraints and Drivers (p. 1-5) Remove degrees of freedom

Actuators and Sensors (p. 1-5)

Force Elements (p. 1-6) Generate interbody forces

Interface Elements (p. 1-6) Interface three-dimensional motion

Utilities (p. 1-7) Miscellaneous useful blocks

Represent machines and bodies

Initiate, impose, and m easure mechanical m otions

with one-dimensional domains in Simscape™

1 Block Reference

Machines, Bodies, and Grounds

Body Represent customizable rigid body

Joints

Ground

Machine Environment

Shared Envir

Assembled Joints (p. 1-2) Collocated joints

Disassembled Joints (p. 1-4)

Massless Connectors (p. 1-4)

onment

Represent immo World

Set up mechani machine

Connect two m so that they environmen

Dislocated joints

Rigidly separated joints

bile point at rest in

cal environment for

echanical components

share same mechanical

Assembled Joints

Bearing Represent composite joint with o ne

translational and three rotational DoFs

1-2

Bush

tom Joint

Cus

ing

esent composite joint with three

Repr

nslational and three rotational

tra

DoF

Represent customizable com posite joint w ith up to three translational and up to three rotational degrees of freedom

Joints

Cylindrical

Represent composite joint with one translational DoF and one rotational DoF, with parallel translation and rotation axes

Gimbal

Represent composite joint with three rotational DoFs

In-Plane Represent composite joint with two

translational DoFs

Planar Represent composite joint with

two translational DoFs and one rotational DoF, with rotational axis orthogonal to plane of translational axes

Prismatic Represent prismatic joint with one

translational degree of freedom

Revolute Represent assembled revolute joint

with one rotational d egre e of freedom

Screw

Represent composite joint with one translational DoF and one rotational DoF, with parallel translation and rotation axes and linear pitch constraint between translational and rotational m otion

Six-DoF

Represent composite joint with three translational and three rotational DoFs

Spherical

Represent assembled spherical joint with three rotational degrees of freedom

Telescoping Represent composite joint with one

translational and three rotational DoFs

1-3

1 Block Reference

Universal Represent composite joint with two

rotational DoFs

Weld Represent joint with no DoFs

Disassembled Joints

Disassembled Cylindrical

Disassembled Prismatic Represent disassembled prismatic

Disassembled Revolute Represent disassembled revolute

Disassembled Spherical

Represent disassembled cylindrical joint, with one translational DoF and one rotational DoF along and about misaligned axes, with no constraints

joint with one translational degree o f freedom along misaligned axes

joint with one rotational degree of freedom about misaligned axes

Represent disassembled spherical joint with three rotational degrees of freedom about dislocated pivots

Massless Connectors

Revolute-Revolute Represent composite joint composed

of two revolute primitives spatially separated by massless connector of constant length

Revolute-Spherical

Represent composite joint composed of revolute and spherical primitives spatially separated by massless connector of constant length

1-4

Spherical-Spherical

Represent composite joint composed of two spherical primitives spatially separated by massless connector of constant length

Constraints and Drivers

Angle Driver Specify angle between two body axis

Constraints and Drivers

vectorsasfunctionoftime

Actua

Distance Driver

Gear Constraint Constrain rotational motion of two

Linear Driver

Parallel Constraint Constrain body axis vectors of two

Point-Curve Constraint Constrain motion of point on o ne

Velocity Driver

tors and Sensors

Body Actuator Apply f orce or torque to body

Specify distance b etw een two Body CS origins as function of time

bodies to move along tangent pitch circles

Specify component of vector difference of two Body CS origins as function of time

bodies to be parallel

body to be along curve on another body

Specify linear combination of the linear and angular velocities of two bodies as function of time

sure body motion

Body Sensor

Constraint & Driver Sensor Measure constraint force or torque

Driver Actuator Apply relative motion betw een a pair

Joint Actuator Apply force, torque, or motion to

Mea

between pair of constrained bodies

of constrained bodies through driver

joint primitive

1-5

1 Block Reference

Joint Initial Condition Actuator Apply initial positions and velocities

to primitives of Joint before starting simulation

Joint Sensor Measure motion of and force or

torque on joint primitive

Joint Stiction Actuator Apply classical friction to joint

primitive

Variable Mass & Inertia Actuator

Force Elements

Body Spring & Damper Model dampe d linear oscillator force

Joint Spring & Damper Model damped linear oscillator force

Interface Elements

Prismatic-Translational Interface Connect prismatic primitive

Vary mass and inertia on body at specific Body coordinate system as function of time (not including thrust force or torque)

between two b od ies

or torque on prismatic or revolute joint between two bodies

to one-dimensional Simscape mechanical translational elements

1-6

Revolute-Rotational Interface Connect revolute primitive

to one-dimensional Simscape mechanical rotational elements

Utilities

Continuous Angle Convert discontinuous, bounded

angular output from sensor to continuous, unbounded angular output

Mechanical Branching Bar Map multiple sensor or actuator

lines to one sensor or actuator port on Joint, Constraint, or Driver, or to one Body coordinate sy stem port on Body

RotationM

atrix2VR

Convert 3-by-3 rotation matrix to equivalent VRML form of rotation axis and angle

1-7

1 Block Reference

1-8

Blocks — Alphabetical List

Angle Driver

Purpose Specify angle between two body axis vectors as function of time

Library Constraints & Drivers

Description The Angle Driver block drives axis vectors defined on two Bodies. You

specify fixed base and fixed follower body axis vectors a Body CS on e ither side of the Driver on each body, then drive the angle between the body axis vectors as a function of time.

The Angle Driver block specifies the angle θ defined by

cos = | |/(| || |)



aa a a⋅

BF B F

as a function of time: θ = θ(t=0) + f(t). You connect the Angle Driver to a Driver Actuator block.

The Simulink time-dependent driving function f(t) and its first two derivatives, as well as their units. If you do not actuate An gle Driver, this block acts a s a time-independent constraint that freezes the angle between the two body axes at its initial value θ(t=0) during the simulation.

input signal into the Driver Actuator specifies the

, aFin the

2-2

Drivers restrict relative degrees of free dom (DoFs) between a pair of bodies as specified functions of time. Locally in a machine, they replace a Joint as the expression of the DoFs. Globally, Driver blocks must occur topologically in closed loops. Like Bodies connected to a Joint, the two Bodies connected to a Drivers are ordered as base and follower, fixing the direction of relative motion.

Caution

If the two axes come close to aligning, that is, if θ approaches zero, the constraint between the two axes becomes singular, and the simulation slows down. See “How SimMechanics™ Software Works” and “Handling Motion Singularities”.

Dialog Box a nd Parameters

Angle Driver

You can also connect a Constraint & Driver Sensor to any Driver measure the reaction forces /torques between the driven bodies.

Connection Parameters

The dialog has two active areas, Connection parameters and Parameters.

The base (B)-follower (F) Body sequence determines the sense of positive motion. Positive rotation is the follower rotating in the right-handed sense about the rotation axis.

Current base

When you connect the base (B) connector port on the Angle Driver block to a Body CS Port on a Body, this param eter is automatically reset to the name of this Body CS. See the following figure, Angle Driver Base and Follow er Body Connector Ports o n page 2-4.

Current follower

When you connect the follower (F) connector port on the Angle Driver block to a Body CS Port on a Body, this parameter is

2-3

Angle Driver

automatically reset to the name of this Body CS. See the following figure, Angle Driver Base and Follower Body Connector Ports on page 2-4.

Number of sensor/actuator ports

Using this spinner menu, you can set the number of extra connector ports needed for connecting Driver Actuator and Constraint & Driver Sensor blockstothisDriver. Thedefaultis

To activate the Driver, connect a Driver Actuator.

Angle Driver Base and Follower Body Connector Ports

Parameters Fixed axis [x y z]

For the Base and Follower bodies, respectively, enter the body axis vectors. The defaults are

[1 0 0].

2-4

See Al

Reference CS

Using the pull-down menu, choose the coordinate system (World, the base Body CS, or the follower Body CS) whose coordinate axes the Base and Follower body axis vectors are oriented w ith respect to. This CS also determines the absolute meaning of reaction forces/torques at this Driver. The defaults are

raint & Driver Sensor, Driver Actuator, Parallel Constraint,

Const

ity Driver

Veloc

Constraining and Driving Degrees of Freedom” for more on

See “

ricting DoFs with Drivers.

rest

Verifying Model Topology” and “How SimMechanics Software

See “

s” for more on u sing drivers in closed loops.

Work

“Constraints and Drivers” on page 1-5.

See

World.

Bearing

Purpose Represent composite joint with one translational and three rotational

DoFs

Library Joints/Assembled Joints

Description The Bearing block represents a composite joint with one translational

degree of freedom (DoF) as one prismatic primitive and three rotational DoFs as three revolute primitives. There are no constraints among the primitives. Unlike Telescoping, Bearing represents the rotational DoFs as three revolutes, rather than as one spherical.

Warning

A joint with three revolute primitives becomes singular if two or three of the rotation axes become parallel (“gimbal lock”). The simulation stops with an error in this case.

A joint with three revolute primitives must be configured in the initial state with the three revolute primitive axes mutually orthogonal. There are no restrictions on the primitive axes once the simulation starts, except to prevent any two of the primitive axes from becoming parallel.

Note Bearings are often represented by one translational and one rotational DoF. The Bearing block has three rotational degrees of freedom, rather than one, in order to represent transverse “play” in the joint.

2-5

Bearing

2-6

Satisfying Joint Requirements

A Joint block represents the relative degrees of freedom between two bodies, not the bodies themselves.

You must connect any Joint block to two and only two Body blocks, the base and the follower. All Joints have tw o connector ports for these connections, defining the direction of joint motion (base to follower). You connect each side of the Joint block to these Body blocks at a Body coordinate system (CS) port.

You specify the joint primitive axes, if any, in the Joint d i alog.

mbly Restrictions on Assembled Joints

Asse

s Joint block is assembled and places restrictions on the connected

Thi

yCSs.

Bod

Bearing

• If the Joint has no pri smatic primitives, the origins of the connected

Body CSs on either side of the Joint must be spatially collocated points, to within assembly tolerances.

• If the Joint has one or more prismatic primitives, the origins of the

connected Body CSs must lie in the span of the prismatic axes:

Dialog Box a nd Parameters

Number of Prismatic Primitives

One Along the prim itive axis

Two

Three

Span of Primitive Ax es

Intheplaneoftheprimitiveaxes

Anywhere in three-dimensional space

2-7

Bearing

The dialog has two active areas, Connection parameters and Parameters.

Connection Parameters

The base (B)-follower (F) Body sequence determines the sense of positive motion. Positive translation is the follower moving in the direction of the translation axis. Positive rotation is the follower moving around the rotational axis following the right-hand rule.

Current base

When you connect the base (B) connector port on the Bearing block to a Body CS Port on a Body, this parameter is automatically reset to the name of this Body CS. See the follow ing figure, Bearing Base and Follower Body Connector Ports on page 2-9.

The base Body is automatically connected to the first joint primitive

Current follower

When you connect the follower (F) connector port on the Bearing block to a Body CS Port on a Body, this param eter is automatically reset to the name of this Body CS. See the following figure, Bearing Base and Follow er Body Connector Ports on page 2-9.

The follower B ody is automatically connected to the last joint primitive

Number of sensor/actuator ports

Using this spinner menu, you can set the number of extra connector ports needed for connecting Joint Actuator and Joint Sensor blocks to this Joint. The default is

R1 in the primitive li st in Parameters.

P1 in the primitive li st in Parameters.

2-8

The motions of prismatic and revolute primitives are specified in linear and angular units, respectively.

Bearing Base and Follower Bod y Connector Ports

Parameters Switch between the Axes and Advanced tabs.

Axes Tab

Name - Primitive

The primitive list states the names and types of joint primitives that make up the Bearing block: revolute primitives and prismatic primitive

Axis of Action [x y z]

Enter here as a three-component vector the directional axes defining the allowed motions of these primitives and their corresponding DoFs:

P1.

Bearing

R1, R2, R3,

• Prismatic: axis of translation

• Revolute: axis of rotation

The d efault vectors are shown in the dialog above. The axis is a directed vector whose overall sign matters.

To prevent singularities and simulation errors, no two of the revolute axes can be parallel.

Reference CS

Using the pull-down menu, choose the coordinate system (World, thebaseBodyCS,orthefollowerBodyCS)whosecoordinateaxes the vector axis of action is oriented with respect to. This CS also determines the absolute meaning of forces/torques and motion along/about the joint axis. The default is

World.

2-9

Bearing

Restricted Parameters

When your model is in Restricted editing mode, you cannot modify the following parameters:

• The Axes (joint primitives) parameters table

The entries on the Axes tab are required. Each DoF primitive in Bearing has an entry line. Thes e lines specify the direction of the axes of action of the DoFs that the Bearing represents.

Advanced Tab

2-10

See

Also

The Advanced tab is optional. You use it to control the way SimMechanics simulation interprets the topology of your schematic diagram.

Mark as the preferred cut joint

In a closed loop, the simulation internally and automatically cuts one and only one joint.

If you want this particular joint to be weighted preferentially for cutting during the simulation, select the check box. The default is not selected.

hing, Cylindrical, Gimbal, Prismatic, Revolute

Bus

Bearing

See “Modeling D egrees of Freedom” for more on representing DoFs with Joints.

See “Verifying Model Topology” and “How SimMechanics Software Works” for more on closed loops and cutting.

2-11

Body

Purpose Represent customizable rigid body

Library Bodies

Description The Body block represents a rigid body with properties you customize.

The representation that you specify must include:

• The body’s mass and moment of inertia tensor

• The coordinates for the body’s center of gravity (CG)

• One or more Body coordinate systems (CSs)

The representation can also include optional body geometry and color information for visualization.

A rigid body is defined in space by the position of its CG (or center of mass) and its orientation in some defined coordinate system.

Setting Body Initial Cond itions The initial position and orientation of a body are set by the entries in its Body dialog that define the body’s home configuration. These initial conditions remain unchanged, unless, with a Joint Initial Condition Actuator, you change the initial conditions of the Joint(s) connected to the Body prior to starting the simulation, or you actuate the Body with a Body Actuator. The imposition of additional initial conditions defines the initial configuration of the body.

2-12

Defining a Body with Mass, Coordinate System, and Visualization Properties

You must enter properties for a SimMechanics body in two sets, mass properties and coordinate system properties.Athirdset,visualization properties,isoptional.

Mass Properties

The mass properties are defined by the body’s mass and inertia tensor.

Body

• The mass is the body’s inertia and controls the translational

acceleration of the CG in response to an a pplied force.

• The inertia tensor measures the distribution of mass density in the

body and controls the rotational acceleration of the body about the CG in response to an applied torque.

• The components of the inertia tensor control the initial orientation of

the body and are always interpreted as being in the CG CS axes. The orientation of the CG CS axes with respect to another CS external to the body (the World CS, a CS on a Ground, or a CS on another Body) then determines the orientation of the body with respect to other bodies or with respect to World.

• The body’s inertia tensor defines its principal axes and moments

and its equivalent ellipsoid, one of the standard shapes available for displaying a body in space.

Coordinate System Properties

The coordinate system properties are defined by the body’s Bod y CSs.

• The CS with its origin at the CG is required. The CG point specifies

both the initial position of the whole body and the origin of the CG CS. You must also orient the CG CS axes.

• You can place one or more additional Body CSs on a body. The Body

dialog requires at least one. You must define each Body CS by the position of its origin and the orientation of its CS axes.

• Each connection of a Joint, Constraint/Drive, Actuator, or Sensor

block to a Body requires an anchor point on the Body. This anchor point is one of the Body CS origins.

• Body CSs on the block available for connections are shown by Body

CS ports CS on the b lock sides.

• The set of a body’s Body CS origins (including the CG CS) defines

the body’s convex hull, one of the standard shapes available for displaying a body in space.

on the sides of the block. You can show or hide each Body

2-13

Body

Visualization Properties

The visualization properties of a body include its color and geometry (surface size and shape).

• As a default, the machine of which the Body is a member determines

these visualization properties.

• You can partly or completely override these defaults with custom

settings for an individual Body.

Default Initial State of a Body

These two properties determine a body’s initia l position and orientation:

• The position of a body’s CG sets its initial position.

• The body’s inertia tensor components (in the CG CS) and the

orientation of the CG CS axes with respect to other CSs in the machine set its initial orientation.

The initial conditions of a machine can be changed with Joint Initial Condition Actuator block s before you start a simulation. If you do not change the initial state of a Body be fore simulation, SimMechanics simulation sets its initial position and orientation to its Body dialog entries, defining the body’s home configuration. SimMechanics simulation also sets the Body’s initial linear/angular velocities to zero in this case.

2-14

Dialog Box a nd Parameters

Body

The dial

Positi Visual

Restri

When y follo

• The P

• The O

og has two active areas, Mass properties and the set of tabs,

on and Orientation for Body coordinate systems, as well as

ization.

cted Para meters

our m odel is in Restricted editing mode, you cannot modify the

wing parameters:

osition Body coordinate systems tab

rientation Body coordinate systems tab

2-15

Body

Mass Properties

Body Coordinate Systems

Mass

Enter the mass of the body in the first field and choose units in the pull-down menu to the right. The mass must be a positive, real number or MATLAB are

1 and kg (kilograms).

Inertia

Enter the inertia tensor (with respect to the Body CG CS axes) in the first field and choose units in the pull-down menu to the right. The tensor must be a 3-by-3 real, symmetric matrix. The default tensor is zero tensor is

kg-m

(kilograms-meters2).

eye(3), the MATLAB 3-by-3 identity matrix. A

zeros(3,3) defines a point mass. The units default

equivalent expression. The defaults

Configuring a Body Coordinate System

You set up Body CSs on the Position and Orientation tabs:

• The default co nfiguration consists of three Body CSs: the re quired CG

CS attached to the body’s CG and two other optional Body CSs, called “CS1” and “CS2,” for connecting Joints, Constraints, or Drivers.

• You can configure the CG CS but not delete it. You also cannot create

additional CG CSs, although you can duplicate the CG CS with a different name. (See more about Body coordinate systems controls following.)

2-16

• The other CSs can be configured or deleted as you want, keeping

at least one.

• Configuring a Body CSs requires two groups of steps:

- Positioning the Body CS origin in the Position tab

- Orienting the Body CS axes in the Orientation tab

• Defining Body CSs requires referring to other, pre-existing CSs in the

model. In a given Body block, you can refer to Body and Grounded CSs in three ways. The references must be to:

- World

- Other Body CSs on the same body

- The Adjoining CS, the coordinate system on a neighboring body

or ground directly connected to the selected Body CS by a Joint, Constraint, or Driver

• You must directly or indirectly define all Body CSs by reference to

a Ground or to World. With indirect reference, you specify a Body CS relative to another CS and so on, in a chain of references that ultimately ends in a Ground or World. The CS reference chains of the Position and Orientation tabs can be different. The CS reference chains must not form a closed cycle.

Body

• Switch between the Position and Orientation tabs.

Each Body CS is labeled with a name,

CS2,etc.,foradditionalCSs.

Configuring the Position Fields

The Position fields for each Body CS specify the position of that CS’s origin as a trans l ation vector:

• The numerical components of the vector carry units.

• The translation vector’s components are oriented with respect to

another set of CS axes.

• The origin is displaced from the origin of another, pre-existing CS in

your machine by this translation vector.

CG for the CG CS, and CS1,

2-17

Body

Highlight each Body CS to configure it.

Origin Position Vector [x y z]

Enter the translation vector that defines the position of the Body CS’s origin.

The entry for the CG CS origin positions the entire body.

Units

Choose linear units for the translation vector. The default is m (meters).

2-18

Translated from Origin of

In the pull-down menu, choose the other, pre-existing CS in your machine that defines the starting point for the translation vector. The choices are this Body. The ending point of the translation vector is this Body CS’s origin.

For the CG CS, the default starting-point CS is additional Body CSs (CS1, CS2, etc.), the default starting point CS is this Body’s

Components in Axes of

In the pull-down menu, choose the CS whose axes define the orientation of the translation vector’s components. The choices are

World, Adjoining, and the other Body CSs on this Body. The

World, Adjoining, and the other Body CSs on

World.Forthe

CG.

Body

translation vector’s components are measured relative to the axes of the CS chosen in this column.

For the CG CS, the default orientation CS is additional Body CSs (CS1, CS2, etc.), the default orientation CS is this Body’s

CG.

World.Forthe

Configuring the Orientation Fields

The Orientation fields for each Body CS specify the orientation of that CS’s triad of axes as a rotation:

• The orientation vector specifying the rotation vector has three

components.

• The numerical components of the vector carry units.

• The rotation is oriented with respect to some other, pre-existing set

of CS coordinate axes in your machine.

• The orie ntation vector’s components are interpreted in the convention

of a rotation representation.

Highlight each Body CS to configure it.

Orientation Vector

Enter the components of the rotation that defines the orientation of the Body CS’s axes. The geometric meaning of these components is determined by the Specified Using Convention column.

2-19

Body

The required entry for the CG CS orients the CG CS axes. Together with the Inertia tensor entry in Mass properties,the CG CS axes orient the whole body with respect to another CS in your machine.

Units

Choose angular units for the rotation, degrees or radians. The default is

deg (degrees).

Relative CS

In the pull-down menu, choose one of the other pre-existing CSs inyourmachinetodefinethestartingorientationfortherotation. The choices are

World, Adjoining, and the other Body CSs on

this Body.

Specified Using Convention

In the pull-down menu, choose the representation type for the rotation:

Rotation Type Orientation Vector Com ponents

Quaternion

3x3Transform

Euler

[

*sin(θ/2) ny*sin(θ/2)

*sin(θ/2) cos(θ/2)]

3-by-3 orthogonal rotation matrix R

Rotation angles about sequence of three axes defining Euler angle convention [first-axis second-axis third-axis]

2-20

Rotation Conventions

There are three conventions in a Body block for representing rotations. See “Body Motion in SimMechanics Representations” and “Body Orientation in SimMechanics Representations” to learn more about rotations.

• Euler

The Euler angle convention specifies the rotation of the Body CS axes by rotating about three axes in a sequence. The components of the 1-by-3 row vector are the angles of rotation about those three axes, respectively in sequence, in degrees or radians.

Body

For example,

Euler X-Y-Z means rotate about the original X axis,

then about the first intermediate Y axis, and then about the second intermediate Z axis. Another example:

Euler X-Z-Y means rotate

about the original X axis, then about the first intermediate Z axis, and then about the second intermediate Y axis.

•

3-by-3 Transform

The transform convention specifies the rotation as a dimensionless 3-by-3 orthogonal rotation matr ix. The inverse of an orthogonal matrix R is equal to its transpose: R

-1

= RT.

The columns of R are the (x,y,z) unit vectors of the Body CS axes. The units menu is inactive.

Quaternion

•

Thequaternionconventionspecifiestherotationinangle-axisform as a dimensionless 1-by-4 row vector:

[nx*sin(θ/2) ny*sin(θ/2) nz*sin(θ/2) cos(θ/2)]

n =(nx,ny,nz) is a three-component vector of unit length: n·n = n

+ n

=1.

The unit vector n specifies the axis of rotation. The rotation angle about that axis is θ and follows the right-hand rule.

Managing the Body Coordinate Systems List

The Body coordinate system controls (see the following figure, Body Coordinate Systems Controls on page 2-23) allow you to add, reorder, and delete Body CSs on a Body block.

2-21

Body

To add a Body CS to the list:

1 Highlight an existing Body CS in the list.

2 Click the Add button (see the following figure, Body Coordinate

Systems Controls on page 2-23).

A new Body CS appears immediately below the Body CS you highlighted. New Body CSs are named in sequence after the current ones: CS3, CS4, etc.

To change the position of a Body CS in the list:

1 Highlight the Body CS whose position you want to change.

2 Click on the Up or Down button (see the following figure, Body

Coordinate Systems Controls on page 2-23) until the Body CS is where you want it.

To delete a Bo dy CS from the list:

2-22

1 Highlight the Body CS you want to delete.

You cannot delete the Body’s CG CS or the last one of the non-CG CSs.

2 Click on the Delete button (see the following figure, B ody Coordinate

Systems Controls on page 2-23).

The Body CS you highlighted disappears.

Body Coordinate Systems Controls

Body

Managing Body CS Ports on a Body Block

Connecting a Joint, Constraint, Driver,Actuator,orSensorblocktoa Body block requires an existing and configured Body CS on that Body:

• These other blocks define, constrain, impart, and measure the motion

of bodies with respect to the origin and coordinate axes of Body CSs. Connect each of these blocks to a Body CS with a connection line.

• The actual connection line running from the other block to the Body

block must be anchored to a displayed Body CS Port the Body block in the model window.

onthesideof

2-23

Body

• A displayed Body CS Port on a Body block indicates a Body CS with

the displayed name configured internally within the Body block.

• Not all the Body CSs configured inside a Body block need to be

displayed, however.

See the preceding figure, Body Coordinate Systems Controls.

Show Port

Select this check box for any Body CS to create a corresponding Body CS Port that line in the Body CS list is now accessible for connection to other blocks.

onthesideoftheBodyblock. TheBodyCSon

2-24

Clear this check box to remove the Body CS Port corresponding to that Body CS on that line in the list.

The defaults are not selected for

To apply your choices to the displayed Body block, click Apply.

Port Side

From the pull-down menu, choose which side of the Body block you want the Body CS Port for that Body CS to be placed on,

Left or Right.

The defaults are

To apply your choices to the displayed Body block, click Apply.

Left for CG and CS1 and Right for CS2.

CG, selected for CS1 and CS2.

Body

Visualization Properties

Default Settings

Visualization settings for a body consist of its

• Body geometry (surface shape)

• Color

The visualization window uses thesesettingstodisplaythebody. By default, a body inherits the visualization settings of the machine to which it is connected.

Customi

You can c menus.

zing the Body Visualization Settings

hange the visualization defaults individually with these

Body ge

From th

•

ometry

epull-downmenu,chooseabodysurfaceshape:

Use ma

Conve

Equi

equi

Exte

Ext

chine default body geomet ry

x hull from Body CS locations

valent ellipsoid from mass properties

valent ellipsoids

rnal graphics file

ernal Graphics File” on page 2-26)

(see “Specifying and Configuring an

(default)

for convex hulls

for

2-25

Body

Body color

From the pull-down menu, choose a body color:

•

Use machine default (default)

Use color palette (see “Specifying a Color from the Color

•

Palette” on page 2-27)

Specifying and Configuring an External Graphics File

2-26

If you cho pull-do

Externa

Attac

ose

wn menu, you must specify some additional information.

l graphics file

In the fi

You can

... but

hedtoBodyCS

In the graph

This

he body geometry. Geometric measurements in the graphics

for t

are interpreted in the units associated with this Body CS.

file

External graphics file in the Body geometry

eld, specify the graphics file.

search for files on your file system by clicking the b row se

ton.

pull-down menu, specify which Body CS to attach the

ics to. Your Body CS list is specified by the Position tab.

Body CS serves as the reference origin and coordinate ax es

Body

Requirements for External Body Geometry Files

Custom body visualization requires a body geometry graphics file in the stereolithographic (STL) format. It supports both binary and ASCII types of the STL format.

See the visualization chapters of the SimMechanics Visualization and Import Guide for a complete discussion of graphics files for specifying body geometries.

Caution

In order for custom visualization to work, this STL file must be either:

• On your MATLAB path.

• In your MATLAB present working folder.

• Specified with complete path in the Body dialog.

Otherwise, visualization reverts to the default body geometry.

Specifying a Color from the Color Palette

If you choose Us e color palette in the Body color pull-down menu, the color palette button appears to the right of the menu. Click the color palette button to select a color for the body.

2-27

Body

See Also Body Actuator, Body Sensor, Ground, Machine Environment,

Mechanical Branching Bar

See the relevant entries in the Glossary: adjoining CS, axis-angle rotation, body, Body CS , center of gravity (CG), convex hull, coordinate system (CS), equivalent ellipsoid, Euler angle s , inertia tensor, mass, principal axes, principal inertial moments, quaternion, right-hand rule, and rotation matrix.

Setting Up and Configuring Bodies in Models

See “Representing Motion” for more details about representing body position and orientation.

See “Modeling Grou nds and Bodies”, “Creating Body CS Ports”, and “About SimMechanics Visualization” for more on setting up Bodies in machines.

See “Applying Motions and Forces” for setting general initial conditions (positions and velocities) of DoFs in a machine.

Visualizing Bodies

2-28

For more about configuring visualization for simulation, see “Starting Visualization and Simulation”. For information about machine and body visualization, including default and custom body geometries and colors, see the SimMechanics Visualization and Import Guide.

Body Actuator

Purpose Apply force or torque to body

Library Sensors & Actuators

Description The Body Actuator block actuates a Body block with a generalized force

signal, representing a force/torque applied to the body:

• Force for translational motion

• Torque for rotational motion

The generalized force is a function of time sp ecif ied by a Simulink input signal. This signal can be any Simulink signal, including a signal feedback from a Sensor block.

The Body Actuator applies the actuation signal in the reference coordinate system (CS) specified in the block dialog.

The inport is the Simulink input signal. The output is the connector port you connect to the Body block you want to actuate.

Tip Carefully distinguish the Body Actuator from the Driver blocks:

• The Body Actuator block applies generalized forces to one body in

a specified reference CS.

• The Driver blocks drive relative degrees of freedom between pairs of

bodies.

Other Ways to Actuate Bodies

The Body Actuator block actuates a Body with force/torque signals only . To actuate a Body with motion signals or initial conditions, or to drive the relative degrees of freedom between a p air of Bodies , see “Actuating a Joint” and “Joint Actuator Example: Body Driver”.

The

mech_body_driver model from the Demos library shows how to

drive the relative DoFs between a pair of bodies. To actuate one body

2-29

Body Actuator

Dialog Box a nd Parameters

alone, use this model and replace the second Body block with a Ground block. To set body initial conditions, replace the second Body block with a Ground block and the Joint Actuators with Joint Initial Condition Actuators.

Thedialoghasoneactivearea,Actuation.

Actuation With respect to CS

Inthepull-downmenu,choosethecoordinatesystem(CS)in which the actuating force/torque is interpreted: either the

(Body CS) Absolute (World).

Generalized Forces

You can apply a force, a torque, or both generalized forces to a body.

If you apply both, you need to bundle the torque and force vectors into a 6-component signal, in the order shown in the dialog.

2-30

Local

to which the Actuator is connected or the default

Applied torque

Select the check box if part or all of the actuating signal is a rotational torque. The default is not selected. The Simulink torque input is a 3-component bundled signal.

In the Units pull-down menu, choose units for the actuating torque. The default is

Applied force

Select the check box if part or all of the actuating signal is a translational force. The default is selected. The Simulink force input is a 3-component bundled signal.

In the Units pull-down menu, choose units for the actuating force. The default is

N (newtons).

N*m (newton-meters).

Example Here is a Body Actuator connected to a Body:

Body Actuator

See

Also

You must connect the Body Actuator to the Body at one of that Body’s attached Body CSs, at the corresponding Body CS Port. The actuation signal acts on the Body at that Body CS’s origin.

y, Body Sensor, Driver Actuator, Joint Actuator, Joint Initial

Bod

dition Actuator, Mechanical Branching Bar

Con

2-31

Body Actuator

See “Body Motion in SimMechanics Representations” for more details on Body coordinate system rotations.

See “Actuating a Joint” and “Joint A ctuator Example: Body Driver”.

See “Machines, Bodies, and Grounds” on page 1-2 and “Constraints and Drivers” on page 1-5.

In Simulink, see the Signal Routing Library and the Sources Library.

2-32

Body Sensor

Purpose Measure body motion

Library Sensors & Actuators

Description The Body Sensor block senses the motion o f a body represented by

a Body block. You connect the BodySensortoaBodycoordinate system (CS) on the Body whose motion you want to sense. The sensor specifically measures the motion of the origin of this Body CS.

The Body Sensor measures the components o f translational and rotational motion in any combination of:

• Translational position, velocity, and acceleration vectors. The

position vector has its tail at the World CS origin.

• Rotational orientation (a 3-by-3 rotation matrix R)andangular

velocity and acceleration vectors

In the block dialog, you choose the reference coordinate system (CS) axes in which these components are represented.

The input is the connector port connected to the Body being sensed. The outport is a set of Simulink signals or one bundled Simulink signal of the selected matrix and/or vector components.

Body Position-Orientation and the Home Configuration

The Body Sensor block can measure the position and/or orientation of a body. It measures these relative to the home configuration of the machine, the machine state before the application of initial condition actuators and assembly of disassembled joints. Thus the Body Sensor includes the effect of the latter, which act before the simulation starts.

Defining Coordinate Representations and Body Orientation

A body’s orientation rotation matrix R relates the components of the same vector v as measured in the inertial W orld CS and in the Body CS by v components measured in the World CS. The column vector v vector v’s three components measured in the Body CS.

=[RT]·vW. The column vector vWlists the vector v’s three

lists the

2-33

Body Sensor

Dialog Box a nd Parameters

The columns of the rotation matrix R are the components of the Body CS unit basis vectors measured w ith respect to the World axes.

See “Body Motion in SimMechanics Representations” and “Body Orientation in SimMechanics Representations” for more details on representing body position and orientation, rotation matrices, and angular velocity.

The dia

log has one active area, Measurements.

Measurements With respect to CS

In the pull-down menu, choose the coordinate system in which the body motion components are represented: either the

CS)

World).

(

2-34

Local (Body

to which the Sensor is connected or the default Absolute

Body Sensor

In the Absolute case, the rotation matrix R and the motion vectors have components represented in the inertial World CS axes. In the premultiplied by the body’s inverse orientation rotation matrix

-1

= RT.

Each vector measurement is a row vector in the Simulink output signal. The selected signals are ordered in the same sequence as the dialog.

Select the check box for each of the possible measurements you want to make:

• Translational motion: Position, Velocity,andAcceleration

vectors: r, v =dr/dt, and a =dv/dt, respectively.

• Rotational motion: Angular velocity and Angular acceleration

vectors and Rotation matrix:

- The Rotation matrix is the 3-by-3 orthogonal rotation matrix R:

Local case, the same body motion components are

RRR

⎛

11 12 13

⎜

RRR

21 22 23

⎜ ⎜

RRR

31 32 33

⎝

representing rotational orientation and satisfying RTR = RRT= I. The components are output columnwise as a 9-component row vector: (R

, R21, R31, R12, ... ).

⎞ ⎟ ⎟

⎟ ⎠

- If you choose the With respect to coordinate system as

Absolute (World, the Rotation matrix measures the body’s

rotational orientation with respect to the World CS. Recall the relationship of vector components in the World and bo dy coordinate axes, v

= R]·vb.

- If you choose the With respect to coordinate system as Local

(Body CS)

matrix R

,theRotation matrix returns the 3-by-3 identity

R = I.

2-35

Body Sensor

- The angular velocity is ω

+(dR/dt)*R

=-R*(dRT/dt), and ε is the permutation symbol. The

= (1/2)Σikε

, where the matrix Ω =

ijkΩik

angular acceleration is α =dω/dt.

In the Units pull-down menus, choose the units for each of the measurements you want:

• Translation: the defaults are

m/s

(meters/second2), respectively, for Position, Velocity,and

m (meters), m/s (meters/second), and

Acceleration.

• Rotation: the defaults are

deg/s (degrees/second) and deg/s

(degrees/second2), respectively, for Angular velocity and Angular acceleration.TheRotation matrix is dimensionless.

Output selected parameters as one signal

Select this check box to convert the output signals into a single bundled signal. The default is selected. If you clear it, the Body Sensor block will grow as many Simulink outports as there are active signals selected, one port for each selected signal.

If the check box is selected, the Simulink signal out has all the active (selected) signals ordered into a single row vector, in the same order you see in the dialog. Nonselected components are removed from the vector signal.

2-36

The sensor outputs are ordered and labeled as follows.

Body Sensor Output Signal Label

Position

Velocity

Angular velocity

Rotation matrix

Acceleration

Angular velocity

[R]

Example Here is a Body Sensor connected to a Body:

Body Sensor

You must co ports. The

nnect the Body Sensor to the Body at one of its Body CS

Sensor measures the motion of that Body CS.

See Also Body, Body Actuator, Constraint & Driver Sensor, Joint Sensor,

Mechanical Branching Bar

See “Kinematics and the Machine’s State of Motion”, “Body Motion in SimMechanics Representations”, and “Body Orientation in SimMechanics Re pre sentations” for more details on representing body position and orientation.

See “Sensing Motions and Forces”.

See the relevant entries in the Glossary about body orientation: axis-angle rotation, Euler angles, rig ht-hand rule, and rotation matrix.

In Simulink, see the Signal Routing Library and the Sinks Library.

2-37

Body Spring & Damper

Purpose Model damped linear oscillator force between two bodies

Library Force Elements

Description The Body Spring & Damper block models the force of a damped spring

acting between two bodies. By Newton’s third law, the spring applies equal and opposite forces to the two bodies. You can use this Force Element b lock to model any linear (Hooke’s law) force with constant coefficients that acts between a pair of bodies.

You connect a Body Spring & Damper between two Body coordinate systems (CSs), each on one body. The vector between the Body CSs defines the direction and length of the spring. One of the Bodies can be a Ground.

Caution

The spring and the damper forces act only along the axis connecting the two Body CSs.

2-38

The Body Spring & Damper has no degrees of freedom (DoFs ).

Grounding the Connected Submachines

The Body Spring & Damper block contains a Shared Environment block. The submachines connected to either side of this block constitute a single composite machine that requires exactly one M achine Environment block, but at least one Ground for each submachine.

Referencing Coordinate Systems on the Connected Bodies

The Body Spring & Damper block is not a Joint and cannot propagate adjoining coordinate systems fromaBodyononesidetoaBodyonthe other side.

One Body is connected to one side of the Body Spring & Damper at one of that Body’s CSs. If you attempt to define that CS in terms of the adjoining CS (the connected CS of the other Body connected to the other side), the first Body cannot detect the connected CS of the second body.

Body Spring & Damper

IfyouneedtodefineadjoiningCSsoneithersideofaBodySpring& Damper, add a Joint block in parallel with the spring-damper.

Adding Joints in Parallel to the Body Spring & Damper

To repres ent the DoFs of one body with respect to the other, either

• Connect one or more Joints in series with the Bodies.

• Create additional Body CSs on each body and connect them with a

Joint in parallel with the Body Spring & Damper. To create parallel grounds, insert additional Ground blocks.

You can add m ore Joint blocks between the Bodies to represent one, two, or three prismatic primitives. Use Prismatic blocks or a Custom Joint block to accomplish this.

Body Spring and Damper Force Law

YouconnectthisblocktoeachBody,A or B, at a Body coordinate system (CS). If r position vector connecting them is r = r is |r|. The relative velocity is v = dr/dt. Then the vector force that body A exerts on body B is

and rBare the positions of these Body CSs, the relative

- rA. The distance of separation

F r rr vrrr=⋅−− −kr b(| | )( / | |) ( )( /| | )

The first term represents the spring or linear displacement force. The second represents the damper or velocity dissipation force, which acts only along the direction of r. Thus the damper is equivalent to a dashpot, not a viscous medium.

You specify

• The spring constant k. A stable s pring requires k >0.

• The natural spring length (offset) r

. The natural length is the length

of the s pring with no forces acting on it and physically m ust be nonnegative: r

≥ 0.

2-39

Body Spring & Damper

• The damping constant b. Adampingrepresentingdissipationand

respecting the second law of thermodynamics requires b ≥ 0. You can use a negative b to represent energy pumping.

Body Spring and Damper Force in Singular Cases

Caution In certain cases, the force formula breaks down, and the block

uses special-case rules to determine the spring-damper force.

To avoid singularities in the initial state of motion, be sure to set the bodies’ initial conditions of position and velocity to physically sensible values.

Singular cases include the following:

• If both r

become singular. The spring force is reprojected along the velocity vector. That is, v/|v|replacesr/|r| in both terms of the force law, once in the f irst term and twice in the second. If the state r = 0 does not persist for more than an instant, this replacement has no effect on the motion.

• If r

undefined. The simulation stops with an error.

and v ≠ 0, and r = 0 at some instant, both terms in the force

≠ 0, and both r and v = 0 at some instant, the force direction is

2-40

Dialog Box a nd Parameters

Body Spring & Damper

Thedialoghastwoactiveareas,Parameters and Units.

Tunable Parameters

All of this block’s fields are tunable during simulation. See the Simulink documentation for more information about tunable parameters.

Parameters Spring constant (k)

Enter the linear spring force constant k. The default is

The units for k are derived implicitly from your choice of position and force units.

Damper constant (b)

Enter the linear damping force constant b. The default is

The units for b are derived implicitly from your choice of velocity and force units.

Spring natural length (r0)

Enter the spring’s natural length (offset) r

.Thedefaultis0.

2-41

Body Spring & Damper

Units Position

In the p ull-down menu, choose units for the relative position vector r.Thedefaultis

Velocity

Inthepull-downmenu,chooseunitsfortherelativevelocity vector v. The default is

Force

In the pull-down menu, choose units for the spring-damper force F acting between the bodies. The default is

Example This is a simple but representative use of the Body Spring & Damper.

m (meters).

m/s (meters/second).

N (newtons).

See Also Body, Body Actuator, Body Sensor, Custom Joint, Ground, Joint Spring

& Damper, Machine Environment, Prismatic, Shared Environment

See “Adding Internal Forces”.

2-42

Bushing

Purpose Represent composite joint with three translational and three rotational

DoFs

Library Joints/Assembled Joints

Description The Bushing block represents a composite joint with three translational

degrees of freedom (DoFs) as three prismatic primitives and three rotational D oFs as three revolute primitives. There are no constraints among the primitives. Unlike Six-DoF, Bushing represents the rotational DoFs as three revolutes, rather than as one spherical.

Warning

A joint with three revolute primitives becomes singular if two or three of the rotation axes becomeparallel(“gimballock”). A joint with two or three prismatic primitives becomes singular if two or three of the translation axes become parallel. The simulation stops with errors in these cases.

Satisfying Joint Requirements

A Joint block represents the relative degrees of freedom between two bodies, not the bodies themselves.

You specify the joint primitive axes, if any, in the Joint d i alog.

2-43

Bushing

Assembly Restrictions on Assembled Joints

This Joint block is assembled and places restrictions on the connected Body CSs.

• If the Joint has no pri smatic primitives, the origins of the connected

Body CSs on either side of the Joint must be spatially collocated points, to within assembly tolerances.

• If the Joint has one or more prismatic primitives, the origins of the

connected Body CSs must lie in the span of the prismatic axes:

Number of Prismatic Primitives

One Along the prim itive axis

Two

Three

Span of Primitive Ax es

Intheplaneoftheprimitiveaxes

Anywhere in three-dimensional space

2-44

Dialog Box a nd Parameters

Bushing

Connection Parameters

The dial

Paramet

Current base

og has two active areas, Connection parameters and

ers.

When you connect the base (B) connector port on the Bushing block to a Body CS Port on a Body, this param eter is automatically reset to the name of this Body CS. See the following figure, Bushing B ase and Follower Body Connector Ports on page 2-46.

2-45

Bushing

The base Body is automatically connected to the first joint primitive

Current follower

When you connect the follower (F) connector port on the Bushing block to a Body CS Port on a Body, this param eter is automatically reset to the name of this Body CS. See the following figure, Bushing B ase and Follower Body Connector Ports on page 2-46.

The follower B ody is automatically connected to the last joint primitive

Number of sensor/actuator ports

Using this spinner menu, you can set the number of extra connector ports needed for connecting Joint Actuator and Joint Sensor blocks to this Joint. The default is

The motions of prismatic and revolute primitives are specified in linear and angular units, respectively.

P1 in the primitive li st in Parameters.

R3 in the primitive li st in Parameters.

Bushing Base and Follower Body Connecto r Por ts

Parameters Switch between the Axes and Advanced tabs.

Axes Tab

ntries on the Axes tab are required. Each DoF primitive in

The e

ing has an entry line. These lines specify the direction of the axes

Bush

tion of the DoFs that the Bushing represents.

of ac

2-46

Name - Primitive

The primitive list states the names and types of joint primitives that make up the Bushing block: prismatic primitives and revolute primitives

Axis of Action [x y z]

Enter here as a three-component vector the directional axes defining the allowed motions of these primitives and their corresponding DoFs:

• Prismatic: axis of translation

• Revolute: axis of rotation

The d efault vectors are shown in the dialog above. The axis is a directed vector whose overall sign matters.

To prevent singularities and simulation errors, no two of the revolute axes and no two of the prismatic axes can be parallel.

Reference CS

R1, R2, R3.

World.

Bushing

P1, P2, P3,

Restricted Parameters

When your model is in Restricted editing mode, you cannot modify the following parameters:

• The Axes (joint primitives) parameters table

2-47

Bushing

Advanced Tab

The Advance SimMechan diagram.

Mark as th

In a close one and on

If you wa cutting is not se

d tab is optional. You use it to control the way

ics simulation interprets the topology of your schematic

e preferred cut joint

d loop, the simulation internally and automatically cuts

ly one joint.

nt this particular joint to be weighted preferentially for

during the simulation, select the check box. The default

lected.

See Also Bearing, Cylindrical, Gimbal, Prismatic, Revolute, Six-DoF

See “Modeling D egrees of Freedom” for more on representing DoFs with Joints.

See “Verifying Model Topology” and “How SimMechanics Software Works” for more on closed loops and cutting.

2-48

Constraint & Driver Sensor

Purpose Measure constraint force or torque between pair of constrained bodies

Library Sensors & Actuators

Description The Constraint & Driver Sensor block me asures the force/torque of

constraint (reaction force/torque) betwe en a pair of bodies. You connect this block to the Constraint or Driver block connected between the two Bodies. The output signal is the reaction force/torque.

The Constraint & Driver Sensor measures the reaction force/torque in the refe rence coordinate system (CS) specified in the block dialog. The Constraint or Driver block connects a base and a follower Body. You choose in the dialog to measure the reaction force/torque on either the base or the follower Body.

The input is the connector port connected to the Constraint or Driver block you want to sense. The outport is a set of Simulink signals or one bundled Simulink signal of the reaction force/torque vector(s).

Physical and Unphysical Reaction Forces Not all the components of the output reaction force/torque signal are significant. Only those components projected into the subspace of the degrees of freedom constrained or driven by the connected Constraint or Driver block are physical. Components orthogonal to the constrained or d riven degrees of freedom are unphysical.

A body’s orientation rotation matrix R relates vector components measured in the body CS and in the inertial World CS by [R]·v The column vector v the body CS. The column vector v measured in the World CS.

lists the vector v ’s three compone nts measured in

lists the vector v’s three components

= vs.

2-49

Constraint & Driver Sensor

Dialog Box a nd Parameters

The dialog has one active area, Measurements.

Measurements Reactions measured on

Inthepull-downmenu,choosetomeasurethereaction force/torque on the base (B) or follower (F) Body. The default is

Base.

2-50

With respect to CS

In the pull-down menu, choose the CS in which the reaction force/torque or motion is interpreted. The default is

World).

(

In the

Absolute case, the force vectors have components measured

relative to the inertial World CS axes. In the force vector signals are premultiplied by the inverse rotation matrix R

Reaction torque

Select the check box if you want to measure the reaction torque. The default is selected. The torque is a row vector in the Simulink output signal.

-1

= RTfor the Body selected in Reactions measured on.

Local case, the same

Absolute

Constraint & Driver Sensor

In the pull-down menu, choose the units for the reaction torque. The default is

Reaction force

Select the check box if you want to measure the reaction force. The default is selected. The force is a row vector in the Simulink output signal.

In the pull-down menu, choose the units for the reaction force. The default is

Output selected parameters as one signal

Select this check box to convert the output signals into a single bundled signal. The default is selected. If you clear it, the Constraint & Driver Sensor block will grow as many Simulink outports as there are active sign als selected, one port for each selected signal.

If the check box is selected, the Simulink signal out has all the active signals bundled into a single row vector, ordered in the order shown in the dialog. The type of the signal components depends on which measurements are active (selected).

N*m (newton-meters).

N (newtons).

The sensor outputs are ordered and labeled as follows.

Constraint & Driver Sensor Output Signal

Reaction torque

Reaction force

Label

Example Here is a Constraint & Driver Sensor connected to a Gear Constraint,

which connects and constraints two Bodies:

2-51

Constraint & Driver Sensor

You must add a Sensor port (connector port) to the Constraint/Driver block to connect the Constraint & D riv er Sensor to it. The base (B)-follower (F) Body sequence on the two sides of the Joint determines the sense of the Constraint & Driver Sensor data.

See Also Body Sensor, Driver Actuator, Joint Sensor, Mechanical Branching Bar

See “Body Mo tion in SimMechanics Representations” and “Sensing Motions and Forces”.

In Simulink, see the Signal Routing Library and the Sinks Library.

2-52

Continuous Angle

Purpose Convert discontinuous, bounded angular output from sensor to

continuous, unbounded angular output

Library Utilities

Description The Continuous Angle block converts a measured angle signal restricted

to the semiopen interval (-180 a continuous, unbounded angle not restricted to any interval. This block requires the angle and the angular velocity as input signals. The continuous, unbounded angle is the output signal.

Caution

Each Continuous Angle block in a model adds a normal Simulink statetothemodel. Usethisblockwithcautionifyouaretrimming or linearizing your model.

The Continuous Angle block does not any additional mechanical states.

The Joint Sensor block outputs the absolute rotational measurement of revolute motion as a bounded angle in the interval (-180 or (-π,+π] radians. Motion that crosses the boundaries of this interval causes discontinuities in the measured angle, from +180 vice versa. Use the Continuous Angle block if you want to convert this restricted angular measurement to an unbo unded measurement.

,+180o] degrees or (-π,+π]radiansto

,+180o] degrees

to -180oor

Dialog Box a nd Parameters

2-53

Continuous Angle

Thedialoghasoneactivearea,Parameters.

Parameters Angle measured in

Choose the units for the input angle and the output continuous angle, either

Rate measured in

Choose the units for the input rate (angular velocity), either (degrees/second) or rad/s (radians/second). The default is deg/s

Example The tutorial “Modeling and Simulating a Closed-Loop Machine”

produces this angular motion output for the Revolute3 and Revolute 2joints:

deg (deg rees ) or rad (radians). The default is deg.

deg/s

2-54

Continuous Angle

The Revolute3 angle is restricted to the interval (-180o, +180o], so values passing either limit of this interval are mapped to the opposite end of the interval. The Revolute2 angle is not restricted, but instead touches genuine turning points in its motion.

After passing the angles and angular velocities through Continuous Angleblocks,theRevolute3angular motion a ppears different:

Revolute3’s motion is unchanged, but its angle is now continuous, w ith no interval restriction. Revolute2’s angle is unchanged.

See Also Joint Sensor

See “Trimming Mechanical Models” and “Linearizing Mechanical Models” for more about states.

2-55

Continuous Angle

See “Utilities” on page 1-7.

2-56

Custom Joint

Purpose Represent customizable composite joint with up to three translational

and up to three rotational degrees of freedom

Library Joints/Assembled Joints

Description The Custom Joint block is a composite joint that you can customize with

a specified combination of primitives (prismatic, revolute, or spherical) representing the most general and unconstrained degrees of freedom (DoFs) in three dimensions:

• Up to three translational DoFs as three prismatic primitives

• Up to three rotational DoFs:

- As a single spherical primitive

- As one, two, or three revolute primitives

The sense of rotational DoFs is defined by the right-hand rule. One spherical or three revolutes together form a right-handed system.

You can add, configure, and delete these primitives from the Custom Joint, w ith a minimum and default of one primitive. The properties of eachprimitivearethesameastheindividualJointsofthesamenames.

Warning

A joint with two or three revolute primitives becomes singular if two or three of the rotation axes become parallel (“gimbal lock”). A joint with two or three prismatic primitives becomes singular if two or three of the translation axes become parallel. The simulation stops with errors in these cases.

2-57

Custom Joint

You can connect Actuator and Sensor blocks to a Custom Joint, with each Actuator and Sensor connecting to an individual primitive. You cannot connect an Actuator to a spherical primitive.

Satisfying Joint Requirements

A Joint block represents the relative degrees of freedom between two bodies, not the bodies themselves.

You specify the joint primitive axes, if any, in the Joint d i alog.

Assembly Restrictions on Assembled Joints

This Joint block is assembled and places restrictions on the connected Body CSs.

• If the Joint has no pri smatic primitives, the origins of the connected

Body CSs on either side of the Joint must be spatially collocated points, to within assembly tolerances.

2-58

• If the Joint has one or more prismatic primitives, the origins of the

connected Body CSs must lie in the span of the prismatic axes:

Number of Prismatic Primitives

One Along the prim itive axis

Two

Three

Span of Primitive Ax es

Intheplaneoftheprimitiveaxes

Anywhere in three-dimensional space

Dialog Box a nd Parameters

Custom Joint

Connection Parameters

The dialog has two active areas, Connection parameters and Parameters.

The base (B)-follower (F) Body sequence determines the sense of positive motion:

• Positive translation is the follower moving in the direction of the

translation axis.

• Positive rotation is the follower rotating in the right-hand rule about

the rotation axis.

• Positive rotation is the follower rotating in the right-hand rule as

shown by the motion figure in the Spherical block reference page.

2-59

Custom Joint

Current base

When you connect the base (B) connector port on the Custom Joint block to a Body CS Port on a Body, this parameter is automatically reset to the name of this Body CS. See the following figure, Custom Joint Base and Follower Body Connector Ports on page 2-60.

The base Body is automatically connected to the first joint primitive in th e primitive list in Parameters.

Current follower

When you connect the follower (F) connector port on the Custom Joint block to a Body CS Port on a Body, this parameter is automatically reset to the name of this Body CS. See the following figure, Custom Joint Base and Follower Body Connector Ports on page 2-60.

The follower B ody is automatically connected to the last joint primitive in th e primitive list in Parameters.

2-60

Number of sensor/actuator ports

Using this spinner menu, you can set the number of extra connector ports needed for connecting Joint Actuator and Joint Sensor blocks to this Joint. The default is cannot be connected to an Actuator.

The motion o f a prismatic primitive is specified in linear units. The motion of a revolute primitive is specified in angular units. The motion of a spherical primitive is three DoFs specified in quaternion form.

Custom Joint Base and Followe r Body Connector Ports

0. A spherical primitive

Parameters Switch between the Axes and Advanced tabs.

Axes Tab

The entries on the Axes tab are required. Each DoF primitive in Custom Joint has an entry line. These lines specify the direction of the axes of action of the DoFs that the Custom Joint represents.

Custom Joint

Name - Pri

In the pu DoF. Up t The rota primiti allowe

The def

Axis o

fAction[xyz]

Enter defin DoF:

• Pris

• Revo

• Sph

mitive

ll-down menu, select a label and primitive type for this

o three prismatic primitives

tional DoFs are represented by up to three revolute

ves:

R1, R2, R3. A spherical primitive S can take all three

d rotational DoFs instead.

ault value is

here as a three-component vector the directional axis

ing the allowe d motion of this primitive and its corresponding

matic: axis of translation

lute: axis of rotation

erical: field is not active

R1 - Revolute.

P1, P2, P3 are allowed.

2-61

Custom Joint

The default vector is [0 0 1]. The axis is a direc ted vector w h ose overall sign matters.

To prevent singularities and simulation errors, no two of the revolute axes and no two of the prismatic axes can be parallel.

Reference CS

The field is not active for a spherical primitive.

Managing the Joint Primitives List in a Custom Joint

The Custom Joint primitives list controls, in the figure, allow you to add, reorder, and delete joint primitives in a Custom Joint block.

World.

2-62

Custom Joint Primitives List Controls

• To add a joint primitive to the primitives list:

- Highlight an existing primitive name in the list.

Custom Joint

- Click on the Add button (see the preceding figure, Custom Joint

Primitives List Controls on page 2-62).

A new primitive will appear immediately below the primitive you highlighted.

• To change the position of a joint primitive in the list:

- Highlight t he primitive whose position you want to change.

- Click on the Up or Down button (see the preceding figure, Custom

Joint Primitives List Controls on page 2-62) until the primitive is where you want it.

• To delete a joint primitive from the list:

- Highlig ht the primitive you want to delete.

- Click on the Delete button (see the preceding figure, Custom Joint

Primitives List Controls on page 2-62).

The primitive you highlighted disappears.

• Custom Joint requires at least one prim itiv e, which you cannot d ele t e.

Restricted Parameters

When your model is in Restricted editing mode, you cannot modify the following parameters:

• The Axes (joint primitives) parameters table

2-63

Custom Joint

Advanced Tab

The Advance SimMechan diagram.

Mark as th

In a close one and on

If you wa cutting is not se

d tab is optional. You use it to control the way

ics simulation interprets the topology of your schematic

e preferred cut joint

d loop, the simulation internally and automatically cuts

ly one joint.

nt this particular joint to be weighted preferentially for

during the simulation, select the check box. The default

lected.

See Also Bushing, Gimbal, Joint Actuator, Joint Initial Condition Actuator, Joint

Sensor, Joint Stiction Actuator, Prismatic, Revolute, Six-DoF, Spherical

See “Modeling D egrees of Freedom” for more on representing DoFs with Joints.

See “Verifying Model Topology” and “How SimMechanics Software Works” for more on closed loops and cutting.

2-64

Cylindrical

Purpose Represent composite joint with one translational DoF and one rotational

DoF, with parallel translation and rotation axes

Library Joints/Assembled Joints

Description The Cylindrical block represents a composite joint with one translational

degrees o f freedom (D oF) as one prismatic primitive and one rotational DoF as one revolute primitive. The translation and rotation axes m ust be parallel.

Satisfying Joint Requirements

A Joint block represents the relative degrees of freedom between two bodies, not the bodies themselves.

You specify the joint primitive axes, if any, in the Joint d i alog.

Assembly Restrictions on Assembled Joints

This Joint block is assembled and places restrictions on the connected Body CSs.

2-65

Cylindrical

• If the Joint has no pri smatic primitives, the origins of the connected

Body CSs on either side of the Joint must be spatially collocated points, to within assembly tolerances.

• If the Joint has one or more prismatic primitives, the origins of the

connected Body CSs must lie in the span of the prismatic axes:

Dialog Box a nd Parameters

Number of Prismatic Primitives

One Along the prim itive axis

Two

Three

Span of Primitive Ax es

Intheplaneoftheprimitiveaxes

Anywhere in three-dimensional space

2-66

Cylindrical

The dialog has two active areas, Connection parameters and Parameters.

Connection Parameters

Current base

When you connect the base (B) connector port on the Cylindrical block to a Body CS Port on a Body, this param eter is automatically reset to the name of this Body CS. See the following figure, Cylindrical Base and Follower Body Connector Ports on page 2-68.

The base Body is automatically connected to the first joint primitive

Current follower

When you connect the follower (F) co nne cto r port on the Cylindrical block to a Body CS Port on a Body, this parameter is automatically reset to the name of this Body CS. See the following figure, Cylindrical Base and Follower Body Connector Ports on page 2-68.

The follower B ody is automatically connected to the last joint primitive

Number of sensor/actuator ports

Using this spinner menu, you can set the number of extra connector ports needed for connecting Joint Actuator and Joint Sensor blocks to this Joint. The default is

P1 in the primitive li st in Parameters.

R1 in the primitive li st in Parameters.

The motions of prismatic and revolute primitives are specified in linear and angular units, respectively.

2-67

Cylindrical

Cylindrical Base and Follower Body Connector Ports

Parameters Switch between the Axes and Advanced tabs.

Axes Tab

The entries on the Axes tab are required. Each DoF primitive in Cylindrical has an entry line. These lines specify the direction of the axes o f action of the DoFs that the Cylindrical represents.

Name - Primitive

The primitive list states the names and types of joint primitives that make up the Cylindrical block: prismatic revolute revolute primitive

R1.

P1 and

2-68

Axis of Action [x y z]

Enter here as a three-component vector the directional axes defining the allowed motions of these primitives and their corresponding DoFs:

• Prismatic: axis of translation

• Revolute: axis of rotation

The default vectors are shown in the dialog above. The axes are directed vectors whose overall sign matters.

The two axes

Reference CS

Using the pull-down menu, choose the coordinate system (World, thebaseBodyCS,orthefollowerBodyCS)whosecoordinateaxes the vector axis of action is oriented with respect to. This CS also

P1 and R1 in Cylindrical must be aligned.

Cylindrical

determines the absolute meaning of forces/torques and motion along/about the joint axis. The default is

Restricted Parameters

When your model is in Restricted editing mode, you cannot modify the following parameters:

• The Axes (joint primitives) parameters table

Advanced Tab

World.

See

Also

The Advanced tab is optional. You use it to control the way SimMechanics simulation interprets the topology of your schematic diagram.

Mark as the preferred cut joint

In a closed loop, the simulation internally and automatically cuts one and only one joint.

If you want this particular joint to be weighted preferentially for cutting during the simulation, select the check box. The default is not selected.

assembled Cylindrical, Prismatic, Revolute, Screw

Dis

“Modeling Degrees of Freedom” for more on representing DoFs

See

hJoints.

wit

2-69

Cylindrical

See “Verifying Model Topology” and “How SimMechanics Software Works” for more on closed loops and cutting.

2-70

Disassembled Cylindrical

Purpose Represent disassembled cylindrical joint, with one translational DoF

and one rotational DoF along and about misaligned axes, with no constraints

Library Joints/Disassembled Joints

Description The Disassembled Cylindrical block represents a composite joint,

one translational and one rotational degrees of freedom (D oF ) along and about a pair of specified misaligned axes between two bodies. SimMechanics simulation automatically assembles (aligns) the two axes at simulation start when it defines a machine’s assembled configuration.

A cylindrical joint is composite, with two DoFs and a single specified axis: a prismatic primitive translating along the axis, and a revolute primitive rotating about the axis. There are no constraints between the two primitives.

Disassembled Cylindrical Axes of Follo wer (blue) and Base (red)

2-71

Disassembled Cylindrical

Satisfying Joint Requirements

A Joint block represents the relative degrees of freedom between two bodies, not the bodies themselves.

You must connect any Joint block to two and only two Body blocks, the base and the follower. All Joints have a default of two connector ports for these connections, defining the direction of joint motion (base to follower). You connect each side of the Joint block to these Body blocks at a Body coordinate system (CS) point.

You specify the joint primitive axes, i f any, in the Joint dialog. The two disassembled primitive joint axes are associated, in order, with the base and follower Bodies, respectively.

You canno t connect an Actuator or Sensor to a D isasse mbled Joint.

Assembly Restrictions on Disassembled Joints

This Joint block is disassemb led: the connected Body CS origins do not need to be spatially collocated points or lie within the span of prismatic primitives, if any.

Dialog Box a nd Parameters

2-72

You can only use a Disassembled Joint block within a closed loop. One loop can have no more than one disassembled joint.

Disassembled Cylindrical

The dialog has two active areas, Connection parameters and Parameters.

Connection Parameters

Current base

When you connect the base (B) connector port on the Disassembled Cylindrical block to a Body CS Port on a Body, this parameter is automatically reset to thenameofthisBodyCS.Seethe following figure, Disassembled Cylindrical Base and Follower Body Connector Ports on page 2-73.

Current follower

When you connect the follower (F) co nne cto r port on the Disassembled Cylindrical block to a Body CS Port on a Body, this parameter is automatically reset to the name of this Body CS. See the following figure, Disassembled Cylindrical Base and Follower Body Connector Ports on page 2-73.

Disasse

mbled Cylindrical Base and Follower Body Connecto r Ports

Parameters There is one Axes tab.

The entries on the Axes tab are required. They specify the directions of the two misaligned axes of the translational-rotational DoFs that the Disassembled Cylindrical represents.

2-73

Disassembled Cylindrical

Name

This column automatically displays the names of the two misaligned rotation axes attached to base and follower bodies, respectively.

Axis of Action [x y z]

Enter here as two three-component vectors the two misaligned directional axes along and about which the base and follower bodies respectively can translate and rotate. The default vectors are

[1 0 0] and [0 1 0], respectively. The axes are directed

vectors whose overall signs matter.

Reference CS

Using t he pull-down menu, choose thecoordinatesystems(World, the base Body CS, or the follower Body CS) whose coordinate axes the two vector axes of translation-rotation are oriented with respect to. The defaults are

Restricted Parameters

When your model is in Restricted editing mode, you cannot modify the following parameters:

World.

• The Axes (joint primitives) parameters table

See Also Cylindrical, Disassembled Prismatic, Disassembled Revolute,

Disassembled Spherical

See “Modeling D egrees of Freedom” for more on representing DoFs with Disassembled Joints.

See “Verifying Model Topology” and “How SimMechanics Software Works” for more on closed loops and cutting disassembled joints.

2-74

Disassembled Prismatic

Purpose Represent disassembled prismatic joint with one tran sl ati onal degree

of freedom alon g misaligned axes

Library Joints/Disassembled Joints

Description The Disassembled Prismatic block r epresents a single translational

degrees of freedom (D oF) along a pair of specified misaligned axes between two bodies. SimMechanics simulation automatically assem bles (aligns) the translation axes at simulationstartwhenitdefinesa machine’s assembled configuration.

Disassembled Prismatic Axes of Follower (blue) and Base (red)

2-75

Disassembled Prismatic

Advanced Tab

The Advance SimMechan diagram.

Mark as th

ics simulation interprets the topology of your schematic

e preferred cut joint

In a close one and on

If you wa cutting is not se

d tab is optional. You use it to control the way

d loop, the simulation internally and automatically cuts

ly one joint.

nt this particular joint to be weighted preferentially for

during the simulation, select the check box. The default

lected.

2-76

Dialog Box a nd Parameters

Disassembled Prismatic

The dialog has two active areas, Connection parameters and Parameters.

Connection Parameters

Current base

When you connect the base (B) connector port on the Disassembled Prismatic block to a Body CS Port on a Body, this parameter is automatically reset to thenameofthisBodyCS.Seethe following figure, Disassembled Prismatic Base and Follower Body Connector Ports on page 2-78.

Current follower

When you connect the follower (F) co nne cto r port on the Disassembled Prismatic block to a Body CS Port on a Body, this parameter is automatically reset to the name of this Body CS. See the following figure, Disassembled Prismatic Base and Follower Body Connector Ports on page 2-78.

2-77

Disassembled Prismatic

Disassembled Prismatic Base and Follower Body Connector Ports

Parameters There is one Axes tab.

The entries on the Axes tab are required. They specify the directions of the two misaligned axes of the translational D oF that the Disassembled Prismatic represents.

2-78

Name

This column automatically displays the names of the two misaligned translation axes attached to base and follower bodies, respectively.

Axis of translation [x y z]

Enter here as two three-component vectors the two misaligned directional axes along which the base and follower bodies respectively can translate. The default vectors are

[0 1 0], respectively. The axes are directed vectors whose overall

signs matter.

Reference CS

Using t he pull-down menu, choose thecoordinatesystems(World, thebaseBodyCS,orthefollowerBodyCS)whosecoordinateaxes the two vector axes of translation are oriented with respect to. The defaults are

World.

[1 0 0] and

Disassembled Prismatic

Restricted Parameters

When your model is in Restricted editing mode, you cannot modify the following parameters:

• The Axes (joint primitives) parameters table

See Also Disassembled Cylindrical, Disassembled Revolute, Disassembled

Spherical, Prismatic

See “Modeling D egrees of Freedom” for more on representing DoFs with Disassembled Joints.

See “Verifying Model Topology” and “How SimMechanics Software Works” for more on clo sing loops with disassembled joints.

2-79

Disassembled Revolute

Purpose Represent disassembled revolute joint with one rotational degree of

freedom about misaligned axes

Library Joints/Disassembled Joints

Description The Disassembled Revolute block represents a single rotational degrees

of freedom (DoF) along a pair of specified misaligned axes between two bodies. SimMechanics simulation automatically assembles (aligns) the rotation axes at simulation start when it defines a machine’s assembled configuration.

2-80

Disassembled Revolute Axes of Follower (blue) and Base (red)

Satisfying Joint Requirements

A Joint block represents the relative degrees of freedom between two bodies, not the bodies themselves.

You must connect any Joint block to two and only two Body blocks, the base and the follower. All Joints have a default of two connector ports

Dialog Box a nd Parameters

Disassembled Revolute

for these connections, defining the direction of joint motion (base to follower). You connect each side of the Joint block to these Body blocks at a Body coordinate system (CS) point.

You specify the joint primitive axes, i f any, in the Joint dialog. The two disassembled primitive joint axes are associated, in order, with the base and follower Bodies, respectively.

You canno t connect an Actuator or Sensor to a D isasse mbled Joint.

Assembly Restrictions on Disassembled Joints

This Joint block is disassemb led: the connected Body CS origins do not need to be spatially collocated points or lie within the span of prismatic primitives, if any.

You can only use a Disassembled Joint block within a closed loop. One loop can have no more than one disassembled joint.

The dialog has two active areas, Connection parameters and

Parameters.

2-81

Disassembled Revolute

Connection Parameters

Current base

When you connect the base (B) connector port on the Disassembled Revolute block to a Body CS Port on a Body, this parameter is automatically reset to the name of this Body CS. See the following figure, Disasse mbled Revolute Base and Follow er Body Conne cto r Ports on page 2-82.

Current follower

When you connect the follower (F) co nne cto r port on the Disassembled Revolute block to a Body CS Port on a Body, this parameter is automatically reset to the name of this Body CS. See the following fig ure, Disassembled Revolute Base and Follower Body Connector Ports on page 2-82.

Disassembled Revolute Ba se and Follower Body Connector Por ts

Parameters There is one Axes tab.

The entries on the Axes tab are required. They specify the directions of the two misaligned axes of the rotational DoF that the Disassembled Revolute represents.

2-82

Disassembled Revolute

Name

This column automatically displays the names of the two misaligned rotation axes attached to base and follower bodies, respectively.

Axis of rotation [x y z]

Enter here as two three-component vectors the two misaligned directional axes about which the base and follower bodies respectively can rotate. The default vectors are

, respectively. The axes are directed vectors whose overall

10]

signs matter.

Reference CS

Using t he pull-down menu, choose thecoordinatesystems(World, thebaseBodyCS,orthefollowerBodyCS)whosecoordinateaxes the two vector axes of rotation are oriented with respect to. The defaults are

Restricted Parameters

When your model is in Restricted editing mode, you cannot modify the following parameters:

World.

[1 0 0] and [0

• The Axes (joint primitives) parameters table

See Also Disassembled Cylindrical, Disassembled Prismatic, Disassembled

Spherical, Revolute

See “Modeling D egrees of Freedom” for more on representing DoFs with Disassembled Joints.

See “Verifying Model Topology” and “How SimMechanics Software Works” for more on clo sing loops with disassembled joints.

2-83

Disassembled Spherical

Purpose Represent d isas semble d spherical joint with three rotational degrees of

freedom about dislocated pivots

Library Joints/Disassembled Joints

Description The Disassembled Spherical block represents three rotational degrees

of freedom (DoF) about a pair of specified dislocated pivots at the two bodies, separated “ball-in-socket” joints. SimMechanics simulation automatically assembles (collocates) the spherical pivots at simulation start when it defines a machine’s assembled configuration.

Two rotational DoFs specify a directional axis, and a third rotational DoF specifies rotation about that directional axis. (See the motion figure in the Spherical block reference page.) The sense of each rotational DoF is defined by the right-hand rule. Unlike the Gimbal block, the Disassembled Spherical block cannot become singular.

2-84

Disassembled Spherical Pivots of Follower (blue) and Base (red)

Satisfying Joint Requirements

A Joint block represents the relative degrees of freedom between two bodies, not the bodies themselves.

Dialog Box a nd Parameters

Disassembled Spherical

follower). You connect each side of the Joint block to these Body blocks at a Body coordinate system (CS) point.

You specify the joint primitive axes, i f any, in the Joint dialog. The two disassembled primitive joint axes are associated, in order, with the base and follower Bodies, respectively.

You canno t connect an Actuator or Sensor to a D isasse mbled Joint.

Assembly Restrictions on Disassembled Joints

This Joint block is disassemb led: the connected Body CS origins do not need to be spatially collocated points or lie within the span of prismatic primitives, if any.

You can only use a Disassembled Joint block within a closed loop. One loop can have no more than one disassembled joint.

Connection Parameters

The dialog has one area, Connection parameters,whichisinactive.

Current base

When you connect the base (B) connector port on the Disassembled Spherical block to a Body CS Port on a Body, this parameter is automatically reset to thenameofthisBodyCS.Seethe following figure, Disassembled Spherical Base and Follower Body Connector Ports on page 2-86.

2-85

Disassembled Spherical

Current follower

When you connect the base (F) connector port on the Disassembled Spherical block to a Body CS Port on a Body, this parameter is automatically reset to thenameofthisBodyCS.Seethe following figure, Disassembled Spherical Base and Follower Body Connector Ports on page 2-86.

Disassembled Spherical Base and Follower Body Connector Ports

See Also Disassembled Cylindrical, Disassembled Prismatic, Disassembled

Revolute, Gimbal, Spherical

See “Modeling D egrees of Freedom” for more on representing DoFs with Disassembled Joints.

2-86

See “Verifying Model Topology” and “How SimMechanics Software Works” for more on clo sing loops with disassembled joints.

Distance Driver

Purpose Specify distance between two Body CS origins as function of time

Library Constraints & Drivers

Description The Distance Driver block drives thedistancebetweentheoriginsof

two Body coordinate system (CS) as a function of time that you specify. This function must always remain nonnegative during the simulation.

Let r

, r2be the vector positions of the origins of CS1 on one Body and

CS2 on the other Body, respectively. These vectors can be measured in anyCS.TheDistanceDriverspecifiesthescalardistanced =|r between these points as a function of time:

- r2|

||()()rr

You connect the D istance Driver to a Driver Actuator block.

The Simulink input signal into the Driver Actuator specifies the time-dependent driving function f(t) and its first two derivatives, as well as their units. If you do not actuate Distance Driver, this block acts as a time-independent constraint that freezes the distance between the two Body CSs at its initial value d(t=0) during the simulation.

Caution

The block computes the initial distance d(t=0) between the coordinate systems when the machine is in its home configuration, the original configuration of the machine’s bodie s before the simulation imposes initial conditions and implements joint assembly.

See “Kinematics and the Machine’s State of Motion” and “How SimMechanics Software Works”.

0 − ==+dt f t

2-87

Distance Driver

Dialog Box a nd Parameters

two Bodies connected to a Drivers are ordered as base and follower, fixing the direction of relative motion.

You can also connect a Constraint & Driver Sensor to any Driver and measure the reaction forces /torques between the driven bodies.

Thedialoghasoneactivearea,Connection parameters.

Connecti Parameters

2-88

The base ( motion. the tran

Curren

Curre

slation axis.

tbase

When yo Driver automa figur on pag

nt follower

When Driv auto figu on p

B)-follower (F) Body sequence determines the sense of positive

Positive translation is the follower moving in the direction of

u connect the base (B) connector port on the Distance

block to a Body CS Port on a Body, this parameter is

tically reset to the name of this Body CS. See the following

e, Distance Driver Base and Follower Body Connector Ports

e2-89.

you connect the follower (F) connector port on the Distance er block to a Body CS Port on a Body, this parameter is matically reset to the name of this Body CS. See the following

re, D istance Driver Base and Follower Body Connector Ports

age 2-89.

Mathworks SIMMECHANICS 3 Reference

Specifications and Main Features

Frequently Asked Questions

User Manual