SimMechanics

Glossary

actuator
An actuator converts a Simulink signal into SimMechanics force/torque or motion signals.

• You can configure a body actuator to apply forces/torques to a body either as an explicit function of time or through feedback forces/torques.
• You can configure a joint actuator to apply forces/torques between the bodies connected on either side of the joint.
• You can configure a driver actuator to apply relative motion between the bodies connected on either side of the driver.
• SimMechanics also has two specialized actuators, one for setting joint initial conditions and one for applying stiction to a joint.

In SimMechanics, an Actuator block has an open round SimMechanics Connector Port for connecting with a Body, Joint, or Driver block and an angle bracket > Simulink inport for connecting with normal Simulink blocks, such as Source blocks for generating force/torque signals.

See also body, Connector Port, driver, initial condition actuator, joint, primitive joint, sensor, and stiction actuator.

adjoining CS
The adjoining CS of a Body CS is the CS on the neighboring body or ground directly connected to the original Body CS by a Joint, Constraint, or Driver.

See also body, Body CS, coordinate system (CS), grounded CS, and World.

assembled joint
Restricts the Body coordinate systems (CSs) on the two bodies at either end of the joint.

• For an assembled prismatic joint, the two Body CS origins must lie along the prismatic axis. The two Bodies translate relatively along the same axis.

• For an assembled joint with multiple prismatic primitives, the two Body CS origins must lie in the plane or space defined by the directions of the prismatic axes.

• For an assembled revolute joint, the two Body CS origins must be collocated. The two Bodies rotate relatively about the same axis.

• For an assembled joint with multiple revolute primitives, the two Body CS origins must be collocated.

• For an assembled spherical joint, the two Body CS origins must be collocated at the spherical primitive's pivot point. The two Bodies pivot relatively about this common origin.

You specify an assembly tolerance for assembled joints, the maximum dislocation distance allowed between all pairs of assembled Body CS origins and the maximum angle of misalignment between all pairs of assembled Body motion axes. If the distance dislocations and/or axis misalignments in an assembled joint grow larger than the assembly tolerance, the simulation stops with an error.

See also assembly tolerance, Body CS, disassembled joint, joint, and primitive joint.

assembly tolerance
Determines how closely an assembled joint must be collocated and aligned. An assembled joint is connected on either side to Body coordinate systems (CSs) on two Bodies and restricts the relative configurations and motions of those Body CSs.

The assembly tolerances set the maximum dislocation of Body CS origins and maximum misalignment of motion axes allowed in assembled joints during the simulation.

• For assembled prismatic primitives, each pair of Body CS origins must lie in the subspace defined by the prismatic axis(es). Each pair of Bodies translates along this (these) common axis(es).
• For assembled revolute primitives, each pair of Body CS origins must be collocated and their respective rotational axes aligned. Each pair of Bodies rotates about this (these) common axis(es).
• For an assembled spherical primitive, the pair of Body CS origins must be collocated. The two Bodies pivot about this common origin.

If the two Body CSs separate or the joint axes misalign in a way that makes their connecting assembled joint primitives no longer respect the assembly tolerances, the simulation stops with an error.

See also assembled joint, Body CS, disassembled joint, and joint.

axis-angle rotation
A representation of a three-dimensional spherical rotation as a rotation axis vector n = (n_x,n_y,n_z) of unit length (n*n = n_x² + n_y² + n_z² = 1) and a rotation angle . Define the rotation axis by the vector n; rotate about that axis by using the right-hand rule.

The rotation axis direction is equivalent to specifying two independent angles; is the third independent angle making up the rotation.

In VRML, you represent body rotations by a vector signal [n_x n_y n_z ].

See also degree of freedom (DoF), Euler angles, primitive joint, quaternion, right-hand rule, rotation matrix, and VRML.

base (base body)
The point from which the joint is directed. The joint directionality runs from base to follower body.

Joint directionality sets the direction and the positive sign of all joint position/angle, motion, and force/torque data.

See also body, directionality, follower (follower body), and right-hand rule.

body
The basic element of a mechanical system or machine. It is characterized by

• Its mass properties (mass and inertia tensor)
• Its position and orientation in space
• Any attached Body coordinate systems

Bodies are connected to one another by joints. Bodies carry no degrees of freedom.

You can attach to a Body block any number of Body coordinate systems (CSs). All SimMechanics Bodies automatically maintain a minimum of one Body CS at the body's center of gravity (CG). The Body block has special axis triad CS ports , instead of the open, round Connector Ports , to indicate the attached Body CSs.

See also actuator, adjoining CS, Body CS, center of gravity (CG), convex hull, coordinate system (CS), degree of freedom (DoF), equivalent ellipsoid, inertia tensor, joint, local CS, mass, and sensor.

Body CS
A local coordinate system (CS) attached to a body, carried along with that body's motion. In general, bodies accelerate as they move, and therefore Body CSs define noninertial reference frames.

You can attach any number of Body CSs to a Body block, and you can choose where to place the Body CS origins and how to orient the Body CS axes. The Body block has special axis triad CS ports instead of the open, round Connector Ports, to give you access to these Body CSs for connecting Joint, Sensor, and Actuator blocks.

Every Body block has an automatic, minimum Body CS at its center of gravity (CG). By default, it also has two other Body CSs for connection to adjacent Joints. The origin and axis orientation of each Body CSs once set by the user during Body configuration, are interpreted as fixed rigidly in that body during the simulation.

See also body, Body CS, center of gravity (CG), convex hull, coordinate system (CS), ground, grounded CS, local CS, reference frame (RF), and World.

center of gravity (CG)
The center of gravity or center of mass of a extended body is the point in space about which the entire body balances in a uniform gravitational field. For translational dynamics, the body's entire mass can be considered as if concentrated at this point.

Every Body block has an automatic, minimum Body coordinate system (CS) with its origin at the CG. This origin point and the Body CS coordinate axes remain fixed rigidly in the body during the simulation.

See also body, Body CS, degree of freedom (DoF), inertia tensor, kinematics, and primitive joint.

CG
See center of gravity (CG).

closed loop system
You can disconnect a closed loop system into two separate systems only by cutting more than one joint. The number of closed loops is equal to the minimum number, minus one, of cuttings needed to disconnect the system into two systems.

See also open system and topology.

composite joint
A joint compounded from more than one joint primitive and thus representing more than one degree of freedom. The joint primitives constituting a composite joint are the primitives of that joint.

A spherical primitive represents three rotational degrees of freedom, but is treated as a primitive.

See also constrained joint, degree of freedom (DoF), joint, and primitive joint

Connection Line
You connect each SimMechanics block to another by using SimMechanics Connection Lines. These lines function only with SimMechanics blocks. They do not carry signals, unlike normal Simulink lines, and cannot be branched. You cannot link Connection Lines directly to Simulink lines.

Connection Lines appear red and dashed if they are not anchored at both ends to a Connector Port . Once you so anchor them, the lines become black and solid.

See also actuator, Connector Port, and sensor.

Connector Port
A special anchor for a Connection Line. Each SimMechanics block has one or more open round SimMechanics Connector Ports for connecting to other SimMechanics blocks. You must connect these round ports only to other SimMechanics round ports. When an open Connector Port is attached to a Connection Line, the Port changes to solid .

A special Connection Port block is provided in the Library Browser to create a round SimMechanics Connector Port for an entire subsystem on that subsystem's boundary.

See also actuator, Connection Line, and sensor.

constrained joint
A composite joint with one or more built-in constraints relating the joint's primitives.

An example is the Screw block, which has a prismatic and a revolute primitive with their motions in fixed ratio. Only one of these degrees of freedom is independent.

See also degree of freedom (DoF), joint, and primitive joint.

constraint
A restriction between degrees of freedom imposed independently of any applied forces/torques. A constraint removes one or more independent degrees of freedom, unless that constraint is redundant and restricts degrees of freedom that otherwise could not move anyway. Constraints can also create inconsistencies with the applied forces/torques that lead to simulation errors.

Constraints are kinematic; that is, they must involve only coordinates and/or velocities. Higher derivatives of coordinates (accelerations, etc.) are determined by the Newtonian force/torque equations and cannot be independently constrained.

Constraints can be holonomic (integrable into a form involving only coordinates) or nonholonomic (not integrable; that is, irreducibly involving velocities).

The relationship specified by a constraint can be an explicit function of time (rheonomic) or not (scleronomic). In SimMechanics, scleronomic constraints are called Constraints, and rheonomic constraints are called Drivers.

SimMechanics Constraint/Driver blocks are attached to pairs of Body blocks.

See also body, degree of freedom (DoF), directionality, and driver.

convex hull
The surface of minimum area with convex (outward-bowing) curvature that passes through all the spatial points in a set. In three dimensions, this set must contain at least four non-coplanar points to make a closed surface with nonzero enclosed volume.

In SimMechanics, the convex hull is an option for visualizing a body. The set of points is all the Body coordinate system (CS) origins configured in that Body block. The visualization of an entire machine is the set of the convex hulls of all its bodies.

If a Body has fewer than four non-coplanar Body CSs, its convex hull is a lower-dimensional figure: three Body CSs produce a triangle without volume; two Body CSs produce a line without area; and one Body CS (the CS at the center of gravity) a point without length.

See also body, Body CS, and equivalent ellipsoid.

coordinate system (CS)
A coordinate system is defined, in a particular reference frame (RF), by a choice of origin and orientation of coordinate axes, assumed orthogonal and Cartesian (rectangular). An observer attached to that CS measures distances from that origin and directions relative to those axes.

SimMechanics has two CS types:

• World: global or absolute inertial CS at rest
• Local CS:
      Grounded CS
      Body CS

See also body, Body CS, convex hull, grounded CS, local CS, reference frame (RF), and World.

CS
A coordinate system (CS).

degree of freedom (DoF)
A single coordinate of relative motion between two bodies. Such a coordinate is free only if it can respond without constraint or imposed motion to externally applied forces or torques. For translational motion, a DoF is a linear coordinate along a single direction. For rotational motion, a DoF is an angular coordinate about a single, fixed axis.

A prismatic joint primitive represents a single translational DoF. A revolute joint primitive represents a single rotational DoF. A spherical joint primitive represents three rotational DoFs in angle-axis form. A weld joint primitive represents zero DoFs.

See also body, coordinate system (CS), dynamics, joint, and kinematics.

directionality
The directionality of a joint, constraint, or driver is its direction of forward motion.

The joint directionality is set by the order of the joint's connected bodies and the direction of the joint axis vector. One body is the base body, the other the follower body. The joint direction runs from base to follower, up to the sign of the joint axis vector. Reversing the base-follower order or the joint axis vector direction reverses the forward direction of the joint.

Joint directionality sets the direction and the positive sign of all joint position/angle, motion, and force/torque data.

Directionality of constraints and drivers is similar, except there is no joint axis, only the base-follower sequence.

See also base (base body), body, follower (follower body), joint, and right-hand rule.

disassembled joint
A disassembled joint does not need to respect the assembly tolerance of your machine.

• For a disassembled prismatic primitive, the Body coordinate system (CS) origins do not have to lie on the prismatic axis. The Bodies translate relatively along misaligned axes.
• For a disassembled revolute primitive, the Body CS origins do not have to be collocated. The Bodies rotate relatively about misaligned axes.
• The a disassembled spherical primitive, the Body CS origins do not have to be collocated. The Bodies pivot relatively about these two dislocated origins.

You can only use disassembled joints in a closed loop, with no more than one per loop.

See also assembled joint, assembly tolerance, closed loop system, and topology.

DoF
A degree of freedom (DoF).

driver
A constraint that restricts degrees of freedom as an explicit function of time (a rheonomic constraint) and independently of any applied forces/torques. A driver removes one or more independent degrees of freedom, unless that driver is inconsistent with the applied forces/torques and leads to a simulation error.

In SimMechanics, you specify the driver function of time in a dialog box in terms of an input Simulink signal from a Driver Actuator.

SimMechanics Driver blocks are attached to pairs of Body blocks.

See also actuator, body, constraint, directionality, and degree of freedom (DoF).

dynamics
A forward dynamic analysis of a mechanical system specifies:

• Topology of how bodies are connected
• Degrees of freedom (DoFs) and constraints among DoFs
• All external forces/torques applied to bodies
• Initial condition of all DoFs:
• Initial linear coordinates and velocities
• Initial angular coordinates and velocities

The analysis then solves Newton's laws to find the system's motion for all later times.

Inverse dynamics is the same, except that the system's motion is specified and the forces/torques necessary to produce this motion are determined.

Dynamics is distinguished from kinematics by explicit specification of externally applied forces/torques.

See also constraint, degree of freedom (DoF), kinematics, and topology.

equivalent ellipsoid
The equivalent ellipsoid of a body is the homogeneous solid ellipsoid, centered at the body's center of gravity, with the same principal moments of inertia and principal axes as the body. A homogeneous solid ellipsoid is the simplest body with, in general, three distinct principal moments.

Every body has a unique equivalent ellipsoid, but a given homogeneous ellipsoid corresponds to an infinite number of other, more complicated bodies. The rotational dynamics of a body depend only on its equivalent ellipsoid (which determines its principal moments and principal axes), not on its detailed shape.

In SimMechanics, the equivalent ellipsoid is an option for visualizing a body.

See also body, convex hull, dynamics, inertia tensor, principal axes, and principal inertial moments.

Euler angles
A representation of a three-dimensional spherical rotation as a product of three successive independent rotations about three independent axes by three independent (Euler) angles.

See also axis-angle rotation, degree of freedom (DoF), primitive joint, quaternion, right-hand rule, and rotation matrix.

follower (follower body)
The point to which the joint is directed. The joint directionality runs from base to follower body.

Joint directionality sets the direction and the positive sign of all joint position/angle, motion, and force/torque data.

See also base (base body), body, directionality, and right-hand rule.

ground
A ground or ground point is a special point fixed at rest in the absolute or global inertial World reference frame.

Each ground has an associated grounded coordinate system (CS). The grounded CS's origin is identical to the ground point, and its coordinate axes are always parallel to the coordinate axes of World.

See also body, coordinate system (CS), grounded CS, and World.

grounded CS
A local CS attached to a ground point. It is at rest in World, but its origin is wherever the ground point is and therefore in general shifted with respect to the World CS origin. The coordinate axes of a grounded CS are always parallel to the World CS axes.

The World coordinate axes are defined so that:

• +x points right

  +y points up (gravity in -y direction)

  +z points out of the screen, in three dimensions

You automatically create a Gounded CS whenever you set up a Ground block.

See also adjoining CS, body, Body CS, coordinate system (CS), ground, local CS, and World.

inertia tensor
The inertia or moment of inertia tensor of an extended rigid body describes its internal mass distribution and the body's angular acceleration in response to an applied torque.

Let V be the body's volume and (r) its mass density, a function of position r within the body. Then the inertia tensor I_ij is:

This tensor is a real, symmetric 3-by-3 matrix or equivalent MATLAB expression.

SimMechanics always assumes the inertia tensor of a body is evaluated in that body's center of gravity coordinate system (CG CS). That is, the origin is set to the body's CG and the coordinate axes are the CG CS axes.

Because the CG CS of a Body block is fixed rigidly in the body during simulation, the values of the inertia tensor components do not change as the body rotates.

See also body, Body CS, equivalent ellipsoid, mass, principal axes, and principal inertial moments.

initial condition actuator
An initial condition actuator gives you a way to move a system's degrees of freedom nondynamically to prepare a system for dynamical integration, in a way consistent with all constraints.

In SimMechanics, the initial conditions are applied to a joint primitive.

See also actuator, dynamics, and kinematics.

joint
Represents one or more mechanical degrees of freedom between two bodies. Joint blocks connect two Body blocks in a SimMechanics schematic. Joints have no mass properties such as mass or an inertia tensor.

A joint primitive represents one translational or rotational degree of freedom or one spherical (three rotational degrees of freedom in angle-axis form). Prismatic and revolute primitives have motion axis vectors. A weld primitive has no degrees of freedom.

A primitive joint contains one joint primitive. A composite joint contains more than one joint primitive.

Joints have a directionality set by their base-to-follower Body order and the direction of the joint primitive axis. The sign of all position/angle, motion, and force/torque data is determined by this directionality.

See also actuator, assembled joint, base (base body), body, composite joint, constrained joint, constraint, degree of freedom (DoF), directionality, disassembled joint, follower (follower body), ground, inertia tensor, massless connector, primitive joint, and sensor.

kinematics
A kinematic analysis of a mechanical system specifies topology, degrees of freedom (DoFs), velocities, and constraints, without explicit specification of externally applied forces/torques or integration of Newton's laws for the system's motion as a function of time.

The kinematic state of a machine at some time is the set of all

• Instantaneous positions
• Instantaneous velocities

of all bodies in the system, for both linear (translational) and angular (rotational) DoFs of the bodies.

Specification of externally applied forces/torques and explicit solution of the system's motion as a function of time are given in the system's dynamics.

See also constraint, degree of freedom (DoF), dynamics, and topology.

local CS
A local coordinate system (CS) is attached to either a Ground or a Body:

• Grounded CS
• Body CS

You define Body CSs when you configure the properties of a Body. A Grounded CS is automatically defined when you represent a ground point by a Ground block.

A grounded CS is always at rest in the World reference frame. The origin of this Grounded CS is the same point as the ground point and therefore in general not the same as the World CS origin.

A Body CS is fixed rigidly in the body and carried along with that body's motion. To indicate an attached coordinate system, a Body block has a special axis triad CS port in place of the open, round Connector Port .

See also body, Body CS, coordinate system (CS), grounded CS, reference frame (RF), and World.

machine precision constraint
A machine precision constraint is maintained on the constrained degrees of freedom to the precision of computer processor arithmetic.

The precision to which the constraint is maintained depends on scale or the physical system of units.

See also constraint, stabilizing constraint, and tolerancing constraint.

mass
The Newtonian mass, the proportionality between a force on a body and the resulting translational acceleration of that body.

Let V be the body's volume and (r) its mass density, a function of position r within the body. Then the mass m is:

The mass is a real, positive scalar or equivalent MATLAB expression.

A body's mass is insensitive to choice of coordinate system origin or coordinate axes orientation.

See also body and inertia tensor.

massless connector
A massless connector is equivalent to two joints whose respective axes are spatially separated by a fixed distance. You can specify the gap distance and the axis of separation. The space between the degrees of freedom is filled by a rigid connector of zero mass.

You cannot actuate or sense a massless connector.

See also disassembled joint and joint.

open system
You can disconnect an open system into two separate systems by cutting no more than one joint.

Such systems can be divided into two types:

• An open chain is a series of bodies connected by joints and topologically equivalent to a line.
• An open tree is a series of bodies connected by joints in which at least one body has more than two joints connected to it. Bodies with more than two connected joints define branch points in the tree. A tree can be disconnected into multiple chains by cutting the branch points.

The end body of a chain is a body with only one connected joint.

See also closed loop system and topology.

physical tree
You obtain the physical tree representation of a machine topology from the full machine topology by removing actuators and sensors and cutting each closed loop once.

See also closed loop system, open system, spanning tree, and topology.

primitive joint
A primitive joint expresses one degree of freedom (DoF) or coordinate of motion.

This DoF can be translation along one direction (prismatic joint) or rotation about one fixed axis (revolute joint).

In SimMechanics, a spherical joint (two rotations to specify directional axis, one rotation about that axis) is also treated as a primitive joint.

These three types of primitive joints are the joint primitives from which composite joints are built up.

A weld primitive has no degrees of freedom.

See also composite joint and joint.

principal axes
The inertia tensor of a body is real and symmetric and therefore can be diagonalized, with three real eigenvalues and three orthogonal eigenvectors. The principal axes of a body are these eigenvectors.

See also equivalent ellipsoid, inertia tensor, and principal inertial moments.

principal inertial moments
The inertia tensor of a body is real and symmetric and therefore can be diagonalized, with three real eigenvalues and three orthogonal eigenvectors. The principal inertial moments or principal moments of inertia of a body are these eigenvalues, the diagonal values when the tensor is diagonalized.

The principal moments of a real body satisfy the triangle inequalities: the sum of any two moments is greater than or equal to the third moment.

If two of the three principal moments are equal, the body has some symmetry and is dynamically equivalent to a symmetric top. If all three principal moments are equal, the body is dynamically equivalent to a sphere.

See also equivalent ellipsoid, inertia tensor, and principal axes.

quaternion
A quaternion represents a three-dimensional spherical rotation as a four-component row vector of unit length:

• q = [n_x*sin(/2) n_y*sin(/2) n_z*sin(/2) cos(/2)],

with q*q = 1. The vector n = (n_x,n_y,n_z) is a three-component vector of unit length: n*n = 1. The unit vector n specifies the axis of rotation. The rotation angle about that axis is and follows the right-hand rule.

The axis-angle representation of the rotation is just [ n ].

See also axis-angle rotation, degree of freedom (DoF), Euler angles, primitive joint, right-hand rule, and rotation matrix.

reference frame (RF)
The state of motion of an observer.

An inertial RF is a member of a set of all RFs moving uniformly with respect to one another, without relative acceleration.

An RF is necessary but not sufficient to define a coordinate system (CS). A CS which requires an origin point and a oriented set of three orthogonal axes.

See also coordinate system (CS), local CS, and World.

RF
A reference frame (RF).

right-hand rule
The right-hand rule is the standard convention for determining the sign of a rotation: point your right thumb into the positive rotation axis and curl your fingers into the forward rotational direction.

See also degree of freedom (DoF), directionality, and joint.

rotation matrix
A representation of a three-dimensional spherical rotation as a 3-by-3 real, orthogonal matrix R: R^TR = RR^T = 1, where R^T is the transpose of R.

In general, R requires three independent angles to specify the rotation fully. There are many ways to represent the three independent angles. Here are two:

• You can form three independent rotation matrices R₁, R₂, R₃, each representing a single independent rotation. Then compose the full rotation matrix R as a product of these three: R = R₃*R₂*R₁. The three angles are Euler angles.
• You can represent R in terms of an axis-angle rotation n = (n_x,n_y,n_z) and , with n*n = 1. Form the antisymmetric matrix :
  
  

• Then Rodrigues' formula simplifies R:
  
  

  The three independent angles are and the two needed to orient n.

See also axis-angle rotation, degree of freedom (DoF), Euler angles, primitive joint, right-hand rule, and quaternion.

schematic diagram
A connected group of SimMechanics blocks. An entire block diagram in a Simulink model window has one or more schematics, each representing a distinct machine.

sensor
Measures the motion of, or forces/torques acting on, a body or joint. A sensor can also measure the reaction forces in a constraint or driver constraining a pair of bodies.

In SimMechanics, a Sensor block has an open round SimMechanics Connector Port for connecting with a Body or Joint block and an angle bracket > Simulink outport for connecting with normal Simulink blocks, such as a Sinks block like Scope.

See also actuator, body, Connector Port, constraint, driver, joint, and primitive joint.

spanning tree
You obtain the spanning tree representation of a machine topology from the full machine topology by removing everything except bodies and joints and cutting each closed loop once.

See also closed loop system, open system, physical tree, and topology.

stabilizing constraint
Modifies the dynamics of a system such that the constraint manifold is attractive, without changing the constrained solution. This constraint solver type is computationally the most efficient.

The precision to which the constraint is maintained depends on scale or the physical system of units.

See also constraint, machine precision constraint, and tolerancing constraint.

stiction actuator
Applies discontinuous friction forces to a joint primitive according to the relative velocity of one body with the other body.

If this relative velocity drops below a specified threshold, the relative motion ceases and the bodies or joints become locked rigidly to one another by static friction.

Above that threshold, the bodies or joints move relative to one another with kinetic friction.

See also actuator, composite joint, dynamics, joint, and primitive joint.

tolerancing constraint
A tolerancing constraint is maintained on the constrained degrees of freedom only up to a specified accuracy and/or precision.

This accuracy/precision is independent of any accuracy/precision limits on the solver used to integrate the system's motion, although constraints cannot be maintained to greater accuracy than the accuracy of the solver.

The precision to which the constraint is maintained depends on scale or the physical system of units.

Tolerancing constraints are useful in realistic simulation of slippage ("slop" or "play") in constraints.

See also constraint, machine precision constraint, and stabilizing constraint.

topology
The global connectivity of the elements of a machine.

For mechanical models, the elements are bodies and the connections are joints, constraints, and drivers. Two topologies are equivalent if you can transform one system into another by continuous deformations and without cutting connections or joining elements.

An open system has no closed loops.

• An open chain is topologically equivalent to a line; and each body is connected to only two other bodies, if the body is internal, or one other body if it is at an end.
• An open tree has one or more branch points. A branch point is where an internal body is connected to more than two other bodies. A tree can be disconnected into multiple chains by cutting at the branch points.

A closed loop system has one or more closed loops. The number of closed loops is equal to the minimum number of joints, minus one, that must be cut to dissociate a system into two disconnected systems.

An actual system can have one of these primitive topologies or can be built up from multiple primitive topologies.

See also body, closed loop system, joint, and open system.

VRML
Virtual Reality Modeling Language, an open, Web-oriented ISO standard for defining three-dimensional virtual worlds in multimedia and the Internet. The Virtual Reality Toolbox uses VRML to create and populate virtual worlds with user-defined bodies.

In VRML, body rotations are represented in the axis-angle form. The SimMechanics RotationMatrix2VR block converts rotation matrices to the equivalent axis-angle forms.

See also axis-angle rotation and the Web3D Consortium online at www.web3d.org.

World
In SimMechanics, World is both the absolute inertial reference frame (RF) and absolute coordinate system (CS) in that RF. World has a fixed origin and fixed coordinate axes that cannot be changed.

The World coordinate axes are defined so that:

• +x points right

  +y points up (gravity in -y direction)

  +z points out of the screen, in three dimensions

See also adjoining CS, coordinate system (CS), ground, grounded CS, and reference frame (RF).

mech_stateVectorMgr

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