SimMechanics

Summary of Technical Vocabulary

These sections summarize the special technical terms used in this guide and point to more detailed definitions in the Glossary:

• Topology of Mechanical Systems
• Coordinate Systems and Reference Frames
• Bodies and Mass Properties
• Joints, Constraints, and Drivers
• Sensors and Actuators

Topology of Mechanical Systems

Mechanical systems can be characterized by their topology, or the global connectivity of their elements. A SimMechanics model's elements are the Body blocks, and the connections are the Joints. A complex system in general is a mixture of these basic topological classes: open systems, with subclasses of open chains and open trees, and closed systems, which contain loops.

Coordinate Systems and Reference Frames

SimMechanics uses a family of coordinate systems (CSs) and reference frames (RFs).

SimMechanics has a built-in inertial RF called World. Ground blocks representing ground points are at rest in this RF. You can think of ground points as fixed points on an infinitely large, immobile body. The World RF defines the state of "no motion" or "at rest" for all systems.

World is also a CS, with an origin and axes:

• +x points right

  +y points up (gravity in -y direction)

  +z points out of the screen, in three dimensions

Users can define additional Local CSs:

• Grounded CSs attached to Ground blocks at rest in the World RF but displaced from the World CS origin
• Body CSs fixed in the system's rigid bodies and moving rigidly with the bodies

In general bodies accelerate as they move. So Body CSs in general live in noninertial RFs.

Bodies and Mass Properties

A body is defined in SimMechanics by its mass properties (mass and inertia tensor), its position and orientation, and user-specified attached Body CSs. Bodies carry no DoFs.

A body's position is specified by the position of its center of gravity (CG). The CG point is also the origin of the body's CG coordinate system (CG CS). The orientation of the CG CS axes is user-specified. The body also can have other Body CSs attached to it. The origins and axes of these CSs are user-specified.

The orientation of the body itself is set by the components of its inertia tensor, which are always interpreted in the body's CG CS axes. The absolute orientation of the body is then determined by the orientation of that body's CG CS axes with respect to World.

Joints, Constraints, and Drivers

Joints carry the degrees of freedom (DoFs) of a system in SimMechanics, but none of its mass or inertia. DoFs represent the possible relative motions between pairs of bodies and are specified by translational and rotational axes. Joints can be primitive or composite, constrained or unconstrained, and assembled or disassembled.

Constraints are functional relationships between the DoFs that hold regardless of applied forces/torques. Drivers are special constraints that specify the motion of DoFs as user-defined functions of time.

Sensors and Actuators

Sensors measure the motions of any body or joint, while actuators specify the motion of a body or joint in various ways. Important specialized Actuator blocks are the following:

• The Joint Actuator, which applies specified motions to a joint
• The Joint Initial Condition Actuator, which specifies a joint's initial conditions for integration
• The Joint Stiction Actuator, which applies static and kinetic friction to joint motion

Sensing Motion and Running the Model

Modeling Mechanical Systems