Kinematic Optimal Design of a 2-DoF Parallel Positioning Mechanism Employing Geometric Algebra

被引：0
作者：
Xinming Huo
Panfeng Wang
Wanzhen Li
机构：
[1] Tianjin University,Key Laboratory of Mechanism Theory and Equipment Design of Ministry of Education
来源：
Advances in Applied Clifford Algebras | 2018年 / 28卷
关键词：
Parallel positioning mechanism; Kinematic analysis; Optimal design; Geometric algebra;
D O I：
暂无
中图分类号：
学科分类号：
摘要：
This paper proposes a geometric algebra (GA) based approach to carry out inverse kinematics and design parameters of a 2-degree-of-freedom parallel mechanism with its topology structure 3-RSR&SS for the first time. Here, R and S denote respectively revolute and spherical joints. The inverse solutions are obtained easily by utilizing special geometric relations of 3-RSR&SS parallel positioning mechanism, which are proven by calculating relations among point, line and plane in virtue of operation rules. Three global indices of kinematic optimization are defined to evaluate kinematic performance of 3-RSR&SS parallel positioning mechanism in the light of shuffle and outer products. Finally, the kinematic optimal design of 3-RSR&SS parallel positioning mechanism is carried out by means of NSGA-II and then a set of optimal dimensional parameters is proposed. Comparing with traditional kinematic analysis and optimal design method, the approach employing GA has following merits, (1) kinematic analysis and optimal design would be carried out in concise and visual way by taking full advantage of the geometric conditions of the mechanism. (2) this approach is beneficial to kinematic analysis and optimal design of parallel mechanisms in automatic and visual manner using computer programming languages. This paper may lay a solid theoretical and technical foundation for prototype design and manufacture of 3-RSR&SS parallel positioning mechanism.
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[1]  
Bayro-Corrochano E(2005)Geometric algebra of points, lines, planes and spheres for computer vision and robotics Robotica 23 755-770
[2]  
Falcon LE(2004)A novel fully decoupled two-degrees-of-freedom parallel wrist ASME J. Mech. Robot. 23 661-667
[3]  
Carricato M(2017)Analytical mobility analysis of bennett linkage using geometric algebra Adv. Appl. Clifford Algebras 27 2083-2095
[4]  
Parenti-Castelli V(2012)Geometric approach for kinematic analysis of a class of 2-DOF rotational parallel manipulators Chin. J. Mech. Eng. 25 24-247
[5]  
Chai XX(1999)Position analysis of a two DOF parallel mechanism–the Canterbury tracker Mech. Mach. Theory 34 599-614
[6]  
Li QC(2013)Solution of inverse kinematics for 6R robot manipulators with offset wrist based on geometric algebra ASME J. Mech. Robot. 5 031010-713
[7]  
Dong X(2008)Inverse kinematics computation in computer graphics and robotics using conformal geometric algebra Adv. Appl. Clifford Algebras 18 699-662
[8]  
Yu JJ(2005)Euclidean geometric objects in the clifford geometric algebra of origin, 3space, infinity Bull. Belg. Math. Soc. Simon Stevin 11 653-1338
[9]  
Chen B(2012)Statics and stiffness model of serial-parallel manipulator formed by $k$ parallel manipulators connected in series ASME J. Mech. Robot. 4 021012-82
[10]  
Zong GH(2017)An analytical approach to determine motions/constraints of serial kinematic chains based on Clifford algebra Proc. Inst. Mech. Eng. Part C J. Mech. Eng. Sci. 231 1324-36
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