THE SIMULATION OF MECHANICAL SYSTEMS WITH A CHANGING TOPOLOGY (KINEMATIC, COLLISIONS, CONNECTIVITY, FORCE CLOSURE)
Abstract
Many mechanical systems are described by discontinuous equations of motion. The discontinuity can be the result of a change in the kinematic constraints between the subsystems. The time and manner of the change in the topology is a function of system dynamics. Thus, the motion of the system and the connectivity changes are difficult to predict. A computer oriented method to automatically predict, detect, and determine how rigid bodies couple and decouple is developed and presented. The method takes advantage of the information provided by the shapes of the rigid bodies (boundaries), state variables, and reaction forces, relieving the user of the task to anticipate the changes in the system connectivity. Therefore it can simulate systems with unpredictable changes in topology. The strategy has the capability to consider the boundaries and shapes of machine parts for unforeseen collisions. The characterization of the changes in topology allows the simulation strategy to function independent of user supplied connectivity changes. The concepts of a point to surface kinematic constraint, force closure, and collision detection, are used to characterize the changes. The equations of motion are reformulated by using an incidence matrix. Even though only planar systems are considered the ideas are applicable to three dimensional systems. The results from the simulation of two example systems are presented. The results demonstrate the strategy's ability to automatically predict, detect, and determine a change in topology, reformulate the equations of motion, maintain the current topological data, indicate the current system mobility, and perform an impact analysis without the user anticipating the changes. The impact analysis handles impact between systems with variable topology and rigid bodies in line contact.
Degree
Ph.D.
Subject Area
Mechanical engineering
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