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History of Robotics Research and Development of Japan2008ManipulationMobility Analysis of Robotic Mechanisms Using Computer Algebra

Keisuke ArikawaKanagawa Institute of Technology
The Kutzbach criterion is widely used for evaluating the mobility of robotic mechanisms. However, this criterion cannot accurately evaluate the mobility of some mechanisms (e.g., overconstrained mechanisms and mechanisms containing passive DOF). We propose a method to automatically evaluate the mobility of robotic mechanisms using computer algebra via the following steps: (1) express the geometrical constraints in a mechanism on the basis of the dual quaternion expression and form simultaneous algebraic equations (SAE) that comprise constraint equations, (2) calculate Groebner bases of the SAE, wherein the variable order is specified such that the joint variables are greater than the hand variables and the term order is specified as lexicographic, and (3) determine mobility by determining the variables that can be freely specified. 24th RSJ Best Paper Award in 2010.
手法概要
Method Overview
変数設定
Parameterization
拘束表現(1)
Representation of Constraint (1)
拘束表現(2)
Representation of Constraint (2)
自由度判定表
Mobility Analysis Table
 

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Correspondence papers

Keisuke Arikawa：Mobility Analysis of Robotic Mechanisms Using Computer Algebra –Basic Algorithm and Application Examples-

Journal of the RSJ, Vol. 27, No. 8, pp. 900-909, 2009 (in Japanese).

Related papers

[1]M.Herve: "The Lie group of rigid body displacements, a fundamental tool for mechanism design," Mechanism and Machine Theory, Vol.34, pp.719-730, 1999.

[2]J.M.Rico and B.Ravani: "On Mobility Analysis of Linkages Using Group Theory," Journal of Mechanical Design, Vol.125, pp.70-80, 2003.

[3]G.Gogu: "Mobility of mechanisms: a critical review," Mechanism and Machine Theory, Vol.40, pp.1068-1097, 2005.

[4]J.S.Dai, Z.Huang and H.Lipkin: "Mobility of Overconstrained Parallel Mechanisms," Journal of Mechanical Design, Vol.128, pp.220-229, 2006.

[5]J.M.Rico and B.Ravani: "On Calculating the Degrees of Freedom or Mobility of Overconstrained Linkages: Single-Loop Exceptional Linkages," Journal of Mechanical Design, Vol.129, pp.301-311, 2007.

[6]J.M.Rico, G.I.Perez, A.Tadeo and C.R.Diez: "Mobility and Overconstraint in Kinematic Chains and Assemblies," Proc. of ASME 2007 IDETC 31st Mechanisms and Robotics Conference, CD-ROM DETC2007-34937, 2007.

[7]A.Muller: "Generic Mobility of Rigid Body Mechanisms," Mechanism and Machine Theory, Vol.44, pp.1240-1255, 2008.

[8]J.Tuomela: "Kinematic Analysis of Multibody Systems," BIT Numerical Mathematics, Vol.48, pp.405-421, 2008.

[9]L.Rolland: "Certified Solving of the Forward Kinematics Problem with an Exact Algebraic Method for the General Parallel Manipulators," Advanced Robotics, Vol.19, No.9, pp.995-1025, 2005.

[10]S.Piipponen, J.Tuomela and T.Arponen: "Kinematical Analysis of Overconstrained Mechanism Using Computational Geometric Algebra," Proc. of ASME 2008 IDETC 32nd Mechanisms and Robotics Conference, CR-ROM DETC2008-49193, 2008.

[11]J.M.McCarthy: "An Introduction to Theoretical Kinematics," The MIT Press, 1990.

[12]C.M.Hoffmann and W.Yang："Compliant Motion Constraints," Proceedings of Asian Symposium on Computer Mathematics, pp.1-16, 2003.

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