Computational Dynamics, 3rd Edition

Chapter 3. KINEMATICS

In the kinematic analysis, we are concerned with studying motion without considering the forces that produce the motion. Unlike the case of dynamic analysis, where the motion of the system due to known forces is determined, the objective of the kinematic analysis is to determine the positions, velocities, and accelerations as the result of known prescribed input motions. Recall that the degrees of freedom of a mechanical system, by definition, are the smallest set of independent coordinates that are required to define the system configuration. If the degrees of freedom and their time derivatives are known, other coordinates and their time derivatives that represent the displacements, velocities, and accelerations of the bodies of the system can be expressed in terms of the system degrees of freedom and their time derivatives. This leads to the displacement, velocity, and acceleration kinematic relationships that can be solved for the state of the system regardless of the forces that produce the motion.

There are three stages that must be followed for the complete kinematic analysis of a mechanical system: position, velocity, and acceleration analyses. In the position analysis, the displacement kinematic relationships are solved assuming that the selected degrees of freedom of the system are specified. These relationships are, in general, nonlinear functions in the system coordinates and their solution may require the use of an iterative numerical procedure such ...