Abstract

Based on the optimization theory and the direct elimination technique, we present a systematic approach to explore the single reciprocal screw axis of Bricard six-revolute mechanisms numerically and to confirm its geometric properties graphically. To overcome the difficulty of deriving the analytical closed-form solutions and the shortcomings of needing an accurate initial estimate and having a highly computational sensitivity in the popular Newton-type procedure, the nonlinear programming algorithm establishes a general computational solution to the matrix displacement equation. Using the transformation of line and screw coordinates and the fundamentals of reciprocity of screws, we develop a simple numerical computational approach to obtain the reciprocal screw axis of mechanisms through the linear dependence or independence of linear algebra. Geometric explanations with 3-D computer graphics are also offered to comprehensively understand their algebraic surface of the reciprocal screw axes and to confirm the correctness and validity of the derived algorithm.

This content is only available via PDF.
You do not currently have access to this content.