Session: MR-02-01 - Theoretical & Computational Kinematics (A.T. Yang Symposium)

Paper Number: 89822

89822 - Numerical Identification of Freedom Spaces Using the Canonical Basis 

In this paper, we introduce a complete set of numerical algorithms to find the principal twists of all freedom spaces given an arbitrary set of desired twists without explicitly constructing the reciprocal constraint space. Principal twists, sometimes referred to as the canonical basis, are the set of twists closest to being mutually orthogonal, parallel, and reciprocal within the twist space. They can be used to categorize freedom spaces by comparing their relative angles and pitches to that of the known forms for each space. The identification of freedom spaces (i.e., twist spaces) has been a central problem in screw theory since its conception. Until now, there has been no autonomous computational tool that identifies, locates, and orients the freedom space that would result from the linear combination any prescribed set of desired degree-of-freedom motions (i.e., twists). The authors are developing this tool as part of an Add-in for SolidWorks to guide users in designing compliant mechanisms via the freedom and constraint topologies (FACT) synthesis approach. The specific contributions of this paper, which were necessary to create this tool, are thus the following: (i) existing analytical methods are converted to complete numerical solutions, (ii) existing numerical tools are made more concise and efficient, (iii) new methods are derived to identify principal twists, and (iv) loose definitions within the field of screw theory are fortified.

Presenting Author: Nigel Archer University of California, Los Angeles

Presenting Author Biography: Nigel is a Ph.D. pre-candidate in the department of Mechanical and Aerospace Engineering at the University of California, Los Angeles. He is currently working on a project with SolidWorks to create a compliant mechanism design Add-in.

Authors:

Nigel Archer University of California, Los Angeles
Jonathan Hopkins University of California, Los Angeles