A Unified Methodology for Mobility Analysis Based on Screw Theory

This chapter presents a unified methodology for mobility analysis based on constraint screw theory. The methodology contains a unified Modified Grubler-Kutzbach Criterion and a set of useful techniques. Firstly, we introduce preliminary fundamentals of screw theory and the Modified Grubler-Kutzbach Criterion with four important techniques. Then, using the Modified Grubler-Kutzbach Criterion and the four techniques, we investigate the mobility analysis of various kinds of mechanisms, including the single-loop mechanism, the symmetrical and asymmetrical parallel mechanism, and complex multiple-loop mechanisms. Universal applicability, validity and quickness of the unified methodology are demonstrated by examples. The proposed methodology is also easy to learn and easy to use for mechanical engineers. Finally, we explain the reason for the validity of this method from the calculation complexity point of view.

[1]  Xia Ping.  Mobility analyses of some "paradoxical mechanisms" including Bennett , 2006 .

[2]  Jean-Pierre Merlet.  Singular Configurations of Parallel Manipulators and Grassmann Geometry , 1989, Int. J. Robotics Res..

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

[4]  R. Clavel,et al.  A Fast Robot with Parallel Geometry , 1988 .

[5]  K. Hao.  Dual number method, rank of a screw system and generation of Lie sub-algebras , 1998 .

[6]  O. Company,et al.  H4: a new family of 4-DOF parallel robots , 1999, 1999 IEEE/ASME International Conference on Advanced Intelligent Mechatronics (Cat. No.99TH8399).

[7]  Z. Huang,et al.  Construction and Kinematic Properties of 3-UPU Parallel Mechanisms , 2002 .

[8]  Han Sung Kim,et al.  Design Optimization of a Cartesian Parallel Manipulator , 2002 .

[9]  Liu Jing-fang.  Mobility analyses of several mechanisms including two novel parallel mechanisms and some “paradoxical” linkages , 2006 .

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

[11]  Q. C. Li,et al.  General Methodology for Type Synthesis of Symmetrical Lower-Mobility Parallel Manipulators and Several Novel Manipulators , 2002, Int. J. Robotics Res..

[12]  K. H. Hunt,et al.  Structural Kinematics of In-Parallel-Actuated Robot-Arms , 1983 .

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

[14]  C. H. Suh,et al.  Kinematics and mechanisms design , 1978 .

[15]  K. H. Hunt,et al.  Kinematic geometry of mechanisms , 1978 .

[16]  Zhen Huang,et al.  The Mobility Analyses of Some Classical Mechanism and Recent Parallel Robots , 2006 .

[17]  Seth Earl Elliott,et al.  The theory of screws , 2022 .

[18]  Q. J. Ge,et al.  A Simple Method for Mobility Analysis Using Reciprocal Screws , 2006 .

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

[20]  Jean-Pierre Merlet,et al.  Parallel Robots , 2000 .

[21]  J.Eddie Baker,et al.  An analysis of the Bricard linkages , 1980 .

[22]  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.

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

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

[25]  Pierre-Luc Richard,et al.  Kinematic Analysis and Prototyping of a Partially Decoupled 4-DOF 3T1R Parallel Manipulator , 2006 .

[26]  J. M. Hervé,et al.  Structural synthesis of 'parallel' robots generating spatial translation , 1991, Fifth International Conference on Advanced Robotics 'Robots in Unstructured Environments.

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

[28]  McCarthy,et al.  Geometric Design of Linkages , 2000 .

[29]  Z. Huang,et al.  Type Synthesis of Symmetrical Lower-Mobility Parallel Mechanisms Using the Constraint-Synthesis Method , 2003, Int. J. Robotics Res..

[30]  G. Gogu.  Chebychev–Grübler–Kutzbach's criterion for mobility calculation of multi-loop mechanisms revisited via theory of linear transformations , 2005 .

[31]  Jack Phillips,et al.  Freedom in machinery , 1984 .