Kinematics and Machine Motion State

About Kinematics

Kinematics is the description of a machine's motion without regard to forces, torques, and the mass properties of bodies. Because accelerations are proportional to forces and torques, if you know the mass properties of the bodies and the forces and torques applied to them, you need only the initial positions and their first derivatives (velocities) to integrate a machine's motion. You should also understand and keep in mind the following related concepts.

Degrees of Freedom

The relative position and orientation of a body with respect to a neighbor constitute up to six degrees of freedom (DoFs). The fundamental DoFs are translational (one body sliding relative to another along a prismatic axis) and rotational (one body rotating relative to another about a revolute axis, or one body pivoting relative to another about a spherical pivot point).

SimMechanics™ DoFs are represented by Joint blocks connected between Body blocks. Bodies without Joints have no DoFs and acquire DoFs only by having Joints connected to them. A SimMechanics machine's motion state is represented by the positions (prismatics), angles (revolutes or sphericals), and their first derivatives with respect to time (velocities).

The State of Motion

The state of motion of a mechanical system is the set of the instantaneous positions and orientations of all its bodies and their linear and angular velocities. SimMechanics body positions/orientations are relative: one body's state is specified with respect to its neighbors. The absolute positions and velocities of the bodies' states are determined via the machine's connections to one or more grounds. These grounds are at rest in World, although they do not have to coincide with the World origin.

Home, Initial, and Assembled Configurations

When you start your model, the SimMechanics simulation configures your machines in preparation for motion by stepping them sequentially through three states.

  • The simulation starts by analyzing the machines in their home configurations. A machine in its home configuration has all its bodies positioned and oriented purely according to the Body block dialog data. All body velocities are zero.

  • From the model's initial condition actuators, the simulation then applies initial condition (position, orientation, and velocity) data to the joints of the model, changing its machines to their initial configurations.

  • Finally, the simulation assembles any disassembled joints in the model, transforming the machines to their assembled configurations. While doing this, it holds fixed any positions and orientations specified by initial condition actuators.

    The assembled configuration is the final premotion machine state.

Updating your SimMechanics diagram (from the Edit menu or by pressing Ctrl+D) resets the model to its currently valid home configuration.

Was this topic helpful?