Computer-aided kinematic synthesis of mechanical systems using configuration space

Min-Ho Kyung, Purdue University

Abstract

This thesis describes a parametric synthesis algorithm for planar mechanical systems comprised of higher kinematic pairs in which each part translates along a fixed axis or rotates around a fixed point. Kinematic functions are computed from the CAD models of the parts and are represented graphically as configuration spaces. The designer can request kinematic changes in the configuration spaces. The program constructs an objective function from the change requests. The objective function is minimized by line search. The line search repeats selection of a search direction and minimization of the objective function along a line with the selected search direction. To select a search direction, we use linear approximation or the conjugate gradient method. In the linear approximation method, the program linearizes contact equations and solves a linear system for a search direction. In the conjugate gradient method (a standard method to solve a quadratic problem), the program uses conjugate vectors as search directions. We use an approximate version of the original conjugate gradient method to minimize the objective function. After the line search has found a new design, the program compares the new kinematics with the initial kinematics by configuration space matching. If it detects an unintended change, it backs up, adds kinematic constraints that prevent the change, and resumes the computation.

Degree

Ph.D.

Advisors

Sacks, Purdue University.

Subject Area

Computer science

COinS