Methods for Force Analysis of Overconstrained Parallel Mechanisms: A Review

The force analysis of overconstrained PMs is relatively complex and difficult, for which the methods have always been a research hotspot. However, few literatures analyze the characteristics and application scopes of the various methods, which is not convenient for researchers and engineers to master and adopt them properly. A review of the methods for force analysis of both passive and active overconstrained PMs is presented. The existing force analysis methods for these two kinds of overconstrained PMs are classified according to their main ideas. Each category is briefly demonstrated and evaluated from such aspects as the calculation amount, the comprehensiveness of considering limbs’ deformation, and the existence of explicit expressions of the solutions, which provides an important reference for researchers and engineers to quickly find a suitable method. The similarities and differences between the statically indeterminate problem of passive overconstrained PMs and that of active overconstrained PMs are discussed, and a universal method for these two kinds of overconstrained PMs is pointed out. The existing deficiencies and development directions of the force analysis methods for overconstrained systems are indicated based on the overview.

[1]  Janusz Frączek,et al.  Joint reactions in rigid or flexible body mechanisms with redundant constraints , 2012 .

[2]  Congzhe Wang,et al.  Multi-objective optimization of a parallel ankle rehabilitation robot using modified differential evolution algorithm , 2015 .

[3]  Yongsheng Zhao,et al.  Theoretical analysis and experiment research of a statically indeterminate pre-stressed six-axis force sensor , 2009 .

[4]  Jorge Angeles,et al.  Minimization of power losses in cooperating manipulators , 1992 .

[5]  Jianfeng Li,et al.  Inverse kinematic and dynamic analysis of a 3-DOF parallel mechanism , 2003 .

[6]  Yongsheng Zhao,et al.  Hyperstatic analysis of a fully pre-stressed six-axis force/torque sensor , 2012 .

[7]  Xiaochun Gao,et al.  A Generalized Stiffness Matrix Method for Force Distribution of Robotic Systems with Indeterminancy , 1993 .

[8]  Zhuming Bi,et al.  Kinetostatic modeling of Exechon parallel kinematic machine for stiffness analysis , 2014 .

[9]  L. Tsai,et al.  Kinematics and Optimization of a Spatial 3-UPU Parallel Manipulator , 2000 .

[10]  Hélène Chanal,et al.  Dynamic model of an overconstrained PKM with compliances , 2013 .

[11]  Jean-Pierre Merlet.  Redundant parallel manipulators , 1996 .

[12]  P. Xirouchakis,et al.  Dynamics analysis of a 3-DOF parallel manipulator with R–P–S joint structure , 2007 .

[13]  Jorge Angeles,et al.  Optimization of dynamic forces in mechanical hands , 1991 .

[14]  Vincenzo Parenti-Castelli,et al.  Static and Stiffness Analyses of a Class of Over-Constrained Parallel Manipulators with Legs of Type US and UPS , 2007, Proceedings 2007 IEEE International Conference on Robotics and Automation.

[15]  Yanzhi Zhao,et al.  Synthesis of branched chains with actuation redundancy for eliminating interior singularities of 3T1R parallel mechanisms , 2016 .

[16]  R. Ledesma,et al.  Augmented lagrangian and mass-orthogonal projection methods for constrained multibody dynamics , 1996 .

[17]  Zhuming Bi,et al.  An Inverse Dynamic Model of Over-Constrained Parallel Kinematic Machine Based on Newton–Euler Formulation , 2014 .

[18]  Hideo Hanafusa,et al.  Contribution of internal forces to the dynamics of closed chain mechanisms , 1995, Robotica.

[19]  Yongsheng Zhao,et al.  A method for force analysis of the overconstrained lower mobility parallel mechanism , 2015 .

[20]  J. Fraczek,et al.  On the unique solvability of a direct dynamics problem for mechanisms with redundant constraints and Coulomb friction in joints , 2011 .

[21]  Yongsheng Zhao,et al.  Internal forces Analysis of the Active Overconstrained Parallel manipulators , 2015, Int. J. Robotics Autom..

[22]  Yongsheng Zhao,et al.  Inverse dynamics and internal forces of the redundantly actuated parallel manipulators , 2012 .

[23]  Janusz Frączek,et al.  Comparison of Selected Methods of Handling Redundant Constraints in Multibody Systems Simulations , 2013 .

[24]  Jun Wu,et al.  Dynamic load-carrying capacity of a novel redundantly actuated parallel conveyor , 2014 .

[25]  David E. Orin,et al.  Control of Force Distribution in Robotic Mechanisms Containing Closed Kinematic Chains , 1981 .

[26]  Yuefa Fang,et al.  Enumeration of a class of overconstrained mechanisms using the theory of reciprocal screws , 2004 .

[27]  Y. F. Zheng,et al.  Optimal Load Distribution for Two Industrial Robots Handling a Single Object , 1989 .

[28]  Jun Wu,et al.  Dynamics and control of a planar 3-DOF parallel manipulator with actuation redundancy , 2009 .

[29]  T. Mruthyunjaya,et al.  Force redundancy in parallel manipulators: Theoretical and practical issues , 1998 .

[30]  L. Tsai,et al.  Jacobian Analysis of Limited-DOF Parallel Manipulators , 2002 .

[31]  Massimo Callegari,et al.  Dynamics modelling and control of the 3-RCC translational platform , 2006 .

[32]  Jorge Angeles,et al.  Real-time force optimization in parallel kinematic chains under inequality constraints , 1991, Proceedings. 1991 IEEE International Conference on Robotics and Automation.

[33]  J. Y. S. Luh,et al.  Coordination of two redundant robots , 1989, Proceedings, 1989 International Conference on Robotics and Automation.

[34]  Andreas Müller,et al.  Internal Preload Control of Redundantly Actuated Parallel Manipulators—Its Application to Backlash Avoiding Control , 2005, IEEE Transactions on Robotics.

[35]  Yong Ming Qian,et al.  Position Equation Establishment and Kinematics Analysis of 3-RRC Parallel Mechanism , 2014 .

[36]  Raffaele Di Gregorio.  Kinematics of the 3-UPU wrist , 2003 .

[37]  Wu Yi Chen,et al.  Research on the Method of Improving Accuracy of Parallel Machine Tools , 2009 .

[38]  Marek Wojtyra,et al.  Joint reactions in rigid body mechanisms with dependent constraints , 2009 .

[39]  Jun Wu,et al.  Dynamic analysis of the 2-DOF planar parallel manipulator of a heavy duty hybrid machine tool , 2007 .

[40]  Dan Zhang,et al.  Dynamic modelling of a 3-DOF parallel manipulator using recursive matrix relations , 2005, Robotica.

[41]  Xianwen Kong.  Standing on the shoulders of giants: A brief note from the perspective of kinematics , 2017 .

[42]  Ron P. Podhorodeski,et al.  Force-unconstrained poses for a redundantly-actuated planar parallel manipulator , 2004 .

[43]  S. Nokleby,et al.  Force capabilities of redundantly-actuated parallel manipulators , 2005 .

[44]  V. Parenti-Castelli,et al.  Dynamics of a Class of Parallel Wrists , 2004 .

[45]  Constantinos Mavroidis,et al.  Analysis of Overconstrained Mechanisms , 1995 .

[46]  W. Blajer.  Augmented Lagrangian Formulation: Geometrical Interpretation and Application to Systems with Singularities and Redundancy , 2002 .

[47]  D. John Sanger,et al.  Redundant grasps, redundant manipulators, and their dual relationships , 1992, J. Field Robotics.

[48]  D. Caldwell,et al.  Geometry and Kinematic Analysis of a Redundantly Actuated Parallel Mechanism That Eliminates Singularities and Improves Dexterity , 2008 .

[49]  S. Staicu,et al.  A novel dynamic modelling approach for parallel mechanisms analysis , 2008 .

[50]  Frank Chongwoo Park,et al.  Design and analysis of a redundantly actuated parallel mechanism for rapid machining , 2001, IEEE Trans. Robotics Autom..

[51]  Marek Wojtyra,et al.  Joint Reaction Forces in Multibody Systems with Redundant Constraints , 2005 .

[52]  Yongjie Zhao,et al.  Dynamic performance comparison of the 8PSS redundant parallel manipulator and its non-redundant counterpart—the 6PSS parallel manipulator , 2009 .

[53]  Bing Zheng,et al.  The weighted generalized inverses of a partitioned matrix , 2004, Appl. Math. Comput..

[54]  Kenneth J. Waldron,et al.  A Solution for the Force Distribution Problem in Redundantly Actuated Closed Kinematic Chains , 1990 .

[55]  R.A. Freeman,et al.  Internal object loading for multiple cooperating robot manipulators , 1989, Proceedings, 1989 International Conference on Robotics and Automation.

[56]  Zexiang Li,et al.  Dynamics and control of redundantly actuated parallel manipulators , 2003 .

[57]  Bo Hu,et al.  Kinematic analysis of two novel 3UPU I and 3UPU II PKMs , 2008, Robotics Auton. Syst..

[58]  S. Staicu,et al.  Inverse dynamics of a 3-PRC parallel kinematic machine , 2012 .

[59]  Zhen Huang,et al.  Kinetostatic Analysis of 4-R(CRR) Parallel Manipulator with Overconstraints via Reciprocal-Screw Theory , 2010 .

[60]  Zhen Huang,et al.  Kinematics/statics of a 4-DOF over-constrained parallel manipulator with 3 legs , 2009 .

[61]  Yongsheng Zhao,et al.  The weighted Moore–Penrose generalized inverse and the force analysis of overconstrained parallel mechanisms , 2017 .

[62]  Vijay R. Kumar,et al.  Force distribution in closed kinematic chains , 1988, IEEE J. Robotics Autom..

[63]  Jun Wu,et al.  Force optimization of planar 2-DOF parallel manipulators with actuation redundancy considering deformation , 2013 .

[64]  Zhiping Xiong,et al.  Note on the weighted generalized inverse of the product of matrices , 2011 .

[65]  Janusz Frączek,et al.  Solvability of reactions in rigid multibody systems with redundant nonholonomic constraints , 2013 .

[66]  Wei Liu,et al.  Development of 6-dof parallel seismic simulator with novel redundant actuation , 2009 .

[67]  Xiaochun Gao,et al.  The Mobility Equation and the Solvability of Joint Forces/Torques in Dynamic Analysis , 1992 .

[68]  Zhen Huang,et al.  The accordance and optimization-distribution equations of the over-determinate inputs of walking machines☆ , 1994 .

[69]  E. J. Haug,et al.  Computer aided kinematics and dynamics of mechanical systems. Vol. 1: basic methods , 1989 .

[70]  Qingsong Xu,et al.  Dynamic modeling and robust control of a 3-PRC translational parallel kinematic machine , 2009 .

[71]  Liping Wang,et al.  Inverse dynamics and simulation of a 3-DOF spatial parallel manipulator , 2003, 2003 IEEE International Conference on Robotics and Automation (Cat. No.03CH37422).

[72]  Zhen Huang,et al.  Dynamic performance analysis of six-legged walking machines , 2000 .

[73]  Jorge Angeles,et al.  Force optimization in redundantly-actuated closed kinematic chains , 1989, Proceedings, 1989 International Conference on Robotics and Automation.

[74]  Jacek Pozorski,et al.  Modelling of turbulent flow in the near-wall region using PDF method , 2003 .

[75]  Zhen Huang,et al.  Kinetostatic model of overconstrained lower mobility parallel manipulators , 2016 .

[76]  Ian D. Walker,et al.  Analysis of Motion and Internal Loading of Objects Grasped by Multiple Cooperating Manipulators , 1991, Int. J. Robotics Res..

[77]  Yongsheng Zhao,et al.  Dynamic loads coordination for multiple cooperating robot manipulators , 2000 .

[78]  Tsuneo Yoshikawa,et al.  Manipulating and grasping forces in manipulation by multifingered robot hands , 1987, IEEE Trans. Robotics Autom..

[79]  Scott B. Nokleby,et al.  Wrench capability analysis of redundantly actuated spatial parallel manipulators , 2009 .

[80]  M. Bergamasco,et al.  Dynamics of parallel manipulators by means of screw theory , 2003 .