Instantaneous mobility analysis using the twist space intersection approach for parallel mechanisms

Abstract This paper focuses on instantaneous mobility analysis of parallel mechanisms using the twist space intersection approach. In this study, a nullspace-associated approach is first presented to determining the intersection of screw systems based on screw theory and linear algebra. The approach provides a way of investigating the motion-screw system of the platform for parallel mechanisms without constraint analysis. By investigating the order of the motion-screw system of a platform, this paper presents the instantaneous mobility of a 3-revolute-prismatic-spherical (3-RPS) parallel mechanism, that of a Bennett mechanism, that of a revolute-cylindrical-prismatic-prismatic (RCPP) mechanism and that of a 3-prismatic-universal-prismatic (3-PUP) parallel mechanism. This way of examining the mobility is equivalent to the way based on constraint analysis, presenting the validity of the presented approach and the correctness of instantaneous mobility analysis using the twist space intersection approach for parallel mechanisms and for overconstrained mechanisms.

[1]  D. R. Kerr,et al.  Finite Twist Mapping and its Application to Planar Serial Manipulators with Revolute Joints , 1995 .

[2]  Yuefa Fang,et al.  Analysis of instantaneous motions of deficient-rank 3-RPS parallel manipulators , 2002 .

[3]  C. Barus.  A treatise on the theory of screws , 1998 .

[4]  Ernesto Rodriguez-Leal,et al.  Kinematic and workspace-based dimensional optimization of a 2-DOF mechanism for a novel multipoint device , 2015 .

[5]  Martin Grübler,et al.  Getriebelehre : Eine Theorie des Zwanglaufes und der ebenen Mechanismen , 1917 .

[6]  J.Eddie Baker.  On mobility and relative freedoms in multiloop linkages and structures , 1981 .

[7]  G. Gogu.  Mobility and spatiality of parallel robots revisited via theory of linear transformations , 2005 .

[8]  Jaime Gallardo-Alvarado,et al.  Lie Algebra and the Mobility of Kinematic Chains , 2003, J. Field Robotics.

[9]  G. Gogu.  Mobility of mechanisms: a critical review , 2005 .

[10]  K. Waldron.  The constraint analysis of mechanisms , 1966 .

[11]  Daniel E. Whitney,et al.  The path method for analyzing mobility and constraint of mechanisms and assemblies , 2005, IEEE Transactions on Automation Science and Engineering.

[12]  Jian S. Dai,et al.  Interrelationship between screw systems and corresponding reciprocal systems and applications , 2001 .

[13]  J. Hervé.  Analyse structurelle des mcanismes par groupe des dplacements , 1978 .

[14]  Jian S. Dai,et al.  Relevance and Transferability for Parallel Mechanisms With Reconfigurable Platforms , 2019, Journal of Mechanisms and Robotics.

[15]  J. Angeles,et al.  DETERMINATION DU DEGRE DE LIBERTE DES CHAINES CINEMATIQUE , 1988 .

[16]  J. Gallardo-Alvarado,et al.  Kinematics and dynamics of a 4-PRUR Schönflies parallel manipulator by means of screw theory and the principle of virtual work , 2018 .

[17]  Jian S. Dai,et al.  Inverse Kinematics and Motion Simulation of a 2-DOF Parallel Manipulator with 3-PUP Legs , 2009 .

[18]  R. Mises.  Motorrechnung, ein neues Hilfsmittel der Mechanik , 2022 .

[19]  J. M. Hervé.  The Lie group of rigid body displacements, a fundamental tool for mechanism design , 1999 .

[20]  Jian S. Dai,et al.  A Linear Algebraic Procedure in Obtaining Reciprocal Screw Systems , 2003, J. Field Robotics.

[21]  J. R. Jones,et al.  Null–space construction using cofactors from a screw–algebra context , 2002, Proceedings of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences.

[22]  J. Dai,et al.  Constraint analysis and bifurcated motion of the 3PUP parallel mechanism , 2012 .

[23]  Qinchuan Li,et al.  Mobility Analysis of Limited-Degrees-of-Freedom Parallel Mechanisms in the Framework of Geometric Algebra , 2016 .

[24]  Xianwen Kong,et al.  Mobility Analysis of Parallel Mechanisms Based on Screw Theory and the Concept of Equivalent Serial Kinematic Chain , 2005 .

[25]  Ting-Li Yang,et al.  A General Formula of Degree of Freedom for Parallel Mechanisms , 2008 .

[26]  Jian S. Dai,et al.  Screw System Analysis of Parallel Mechanisms and Applications to Constraint and Mobility Study , 2004 .

[27]  H. Lipkin,et al.  Mobility of Overconstrained Parallel Mechanisms , 2006 .

[28]  B. Ravani,et al.  On Mobillity Analysis of Linkages Using Group Theory , 2002 .

[29]  J.Eddie Baker,et al.  On relative freedom between links in kinematic chains with cross-jointing , 1980 .

[30]  Jonathan B. Hopkins,et al.  Mobility and Constraint Analysis of Interconnected Hybrid Flexure Systems via Screw Algebra and Graph Theory , 2017 .

[31]  Jing-Shan Zhao,et al.  A theory of degrees of freedom for mechanisms , 2004 .

[32]  Zhen Huang,et al.  A general methodology for mobility analysis of mechanisms based on constraint screw theory , 2009 .