A novel method for the solution of the forward displacement problem of spherical parallel manipulators. Issue 1 (22nd October 2012)

• Record Type: Journal Article
• Authors: Rodriguez, J.; Ruggiu, M.
• Is Part Of: Zeitschrift für angewandte Mathematik und Mechanik. Volume 93:Issue 1(2013)
• Page Start: 73
• Page End: 82
• Publication Date: 2012-10-22
• Subjects: Mathematics -- Periodicals; Mechanics, Applied -- Periodicals; Engineering -- Periodicals; 519
• DOI: 10.1002/zamm.201200059
• Languages: English
• ISSNs: 0044-2267

Abstract

<abstract abstract-type="main" xml:lang="en"> <title>Abstract</title> <p>In this paper, a novel method that solves the Forward displacement problem (FDP) of several common spherical parallel manipulators (SPMs) is presented. The method uses the quaternion algebra to express the FDP as a system of equations and the Dixon determinant procedure to construct univariate polynomials whose roots can be found either numerically or analytically. A case study is solved for a specific SPM, which satisfies certain geometric conditions, having 3 ‐ <underline><italic>R</italic></underline>(<italic>E</italic>)<italic>R</italic> architecture, with <italic>R</italic> denoting a revolute joint, <italic>E</italic> a planar motion generator and underlines indicating the actuated joint. In this case, the solutions of the system are obtained analytically by a symbolic method exploiting symmetries.</p> </abstract>