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An Application of Yaglom's Geometric Algebra to Kinematic Synthesis of Linkages for Prescribed Planar Motion of Oriented Lines

[+] Author and Article Information
Ettore Pennestri

Department of Enterprise Engineering, University of Rome Tor Vergata, via del Politecnico, 1, 00133 Roma − Italy
pennestri@mec.uniroma2.it

Pier Paolo Valentini

Department of Enterprise Engineering, University of Rome Tor Vergata, via del Politecnico, 1, 00133 Roma − Italy
valentini@ing.uniroma2.it

1Corresponding author.

ASME doi:10.1115/1.4038924 History: Received April 27, 2017; Revised December 01, 2017

Abstract

Planar motion coordination of a line passing through a point or tangent to a conic is a well known problem in kinematics. In the analytical treatments the line is usually considered unoriented. In this paper, for the first time, it is explored the use of Yaglom algebraic geometry to deduce the equations of circles tangent to three and four homologous planar positions of oriented lines. The analytical developments are based on the dual number representation of oriented lines in a plane. The paper proposes the application of findings to the kinematic synthesis of planar linkages. It is also demonstrated that, for a general planar motion, there is not any line whose five finitely separated positions share the same concurrency point.

Copyright (c) 2017 by ASME
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