A DH-Parameter Based Condition for 3R Orthogonal Manipulators to Have Four Distinct Inverse Kinematic Solutions

[+] Author and Article Information
P. Wenger, D. Chablat, M. Baili

Institut de Recherche en Communications et Cybernétique de Nantes, UMR CNRS 6597, 1, rue de la Noë, BP 92101, 44312 Nantes Cedex 03, France

J. Mech. Des 127(1), 150-155 (Mar 02, 2005) (6 pages) doi:10.1115/1.1828460 History: Received October 21, 2003; Revised May 11, 2004; Online March 02, 2005
Copyright © 2005 by ASME
Topics: Manipulators
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Orthogonal manipulator in its zero configuration    
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Singularity curves for a quaternary manipulator when (a) a2>a3 and (b) a2<a3
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Continuous deformation of the internal boundary as a3 is decreased (a2=1.5 and d2=0.5). From 1.1 to 0.5, the manipulator is quaternary (a)–(c). From 0.5 to 0.2, two cusps and one node merge into one point with four equal IKS and then disappear: The manipulator turns binary (d)–(e)    
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Graphs of Eqs. (12) and (13) shown in sections of the DH-parameter space. Graph of (12) is shown in bold lines
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The three test manipulators (a) and their workspace (b). Manipulators (1) and (2) are binary whereas (3) is quaternary
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Numerical plots of binary manipulators in the same sections as in Fig. 4
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Plot of the separating surface



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