Hostname: page-component-7c8c6479df-nwzlb Total loading time: 0 Render date: 2024-03-28T13:07:29.370Z Has data issue: false hasContentIssue false

Revisiting screw theory-based approaches in the constraint wrench analysis of robotic systems

Published online by Cambridge University Press:  02 September 2021

Ehsan Sharafian M
Affiliation:
Department of Mechanical Engineering, Amirkabir University of Technology (Tehran Polytechnic), Tehran, Iran Vehicle Technology Research Institute, Amirkabir University of Technology (Tehran Polytechnic), Tehran, Iran
Afshin Taghvaeipour*
Affiliation:
Department of Mechanical Engineering, Amirkabir University of Technology (Tehran Polytechnic), Tehran, Iran
Maryam Ghassabzadeh S
Affiliation:
Department of Mechanical Engineering, Amirkabir University of Technology (Tehran Polytechnic), Tehran, Iran Vehicle Technology Research Institute, Amirkabir University of Technology (Tehran Polytechnic), Tehran, Iran
*
*Corresponding author. E-mail: ataghvaei@aut.ac.ir

Abstract

This paper aims at shedding lights on two approaches that were recently proposed for the constraint wrench analysis of robotic manipulators. Both approaches benefit from the Newton–Euler equations, screw notations, and constraint transformation matrices (CTM) to cope with the inverse dynamic problem of multibody systems. In the first approach, which is called the joint-based method, the constraint transformation matrices are derived directly from the kinematic constraints which are imposed on the rigid links by kinematic pairs. In the second approach, which is referred to as the link-based method; however, the constraint matrices are obtained based on the wrench transfer formula of each rigid link. In this study, by resorting to the definition of reciprocal screws, the former methodology is further enhanced to a new version as well. Moreover, based on the proposed modified joint-based CTM, constraint forces and moments distribution indices are introduced. The three constraint wrench analysis methodologies, two joint-based and one link-based, result in different CTMs and set of equations as well, which will be discussed in detail. In the end, on two case studies, a spherical four-bar linkage and a Delta parallel robot, the pros and cons of all three constraint wrench analysis methodologies are discussed, and the proposed indices will be examined. The numerical results reveal that, although all three methods identically compute the magnitude of the applied and constraint force and moment vectors, the joint-based approaches do not report the constraint components with respect to a specific coordinate frame. Moreover, it is shown that the proposed indices can approximately predict the constraint forces and moments distribution at joints, which can be used as force transmission indicators in multibody systems.

Type
Research Article
Copyright
© The Author(s), 2021. Published by Cambridge University Press

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Sun, T., Lian, B., Song, Y. and Feng, L., “Elastodynamic optimization of a 5-DoF parallel kinematic machine considering parameter uncertainty,” IEEE/ASME Trans. Mechatron. 24(1), 315325 (2019).CrossRefGoogle Scholar
Miller, K., Dynamics of the new UWA robot In, Proc. Australian Conference on Robotics and Automation. (2001).Google Scholar
Pang, H. and Shahinpoor, M., “Inverse dynamics of a parallel manipulator,” Journal of Robotic Systems 11(8), 693702 (1994).CrossRefGoogle Scholar
Staicu, S., “Matrix modeling of inverse dynamics of spatial and planar parallel robots,” Multibody System Dynamics 27(2), 239265 (2012).CrossRefGoogle Scholar
Carp-Ciocardia, D., Dynamic analysis of Clavel’s delta parallel robot In, 2003 IEEE international conference on robotics and automation (Cat. No. 03CH37422). pp. 4116-4121 (IEEE, 2003).Google Scholar
Choi, H.-B., Konno, A. and Uchiyama, M., Inverse dynamic analysis of a 4-DOF parallel robot H4 In, 2004 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS)(IEEE Cat. No. 04CH37566). pp. 3501-3506 (IEEE, 2004).Google Scholar
Mazare, M., Taghizadeh, M. and Najafi, M. R., “Inverse Dynamics of a 3-P [2 (US)],” Transl. Parallel Rob. Rob. 37(4), 708728 (2019).Google Scholar
Enferadi, J. and Jafari, K., “A Kane’s based algorithm for closed-form dynamic analysis of a new design of a 3RSS-S spherical parallel manipulator,” Multibody Sys. Dyn. (2020).CrossRefGoogle Scholar
Kingsley, C. and Poursina, M., “Extension of the divide-and-conquer algorithm for the efficient inverse dynamics analysis of multibody systems,” Multibody Sys. Dyn 42(2), 145167 (2018).CrossRefGoogle Scholar
Mata, V., Provenzano, S., Cuadrado, J. and Valero, F., “Inverse dynamic problem in robots using Gibbs-Appell equations,” Robotica 20(1), 59 (2002).CrossRefGoogle Scholar
Li, Y. and Xu, Q., “Kinematics and inverse dynamics analysis for a general 3-PRS spatial parallel mechanism,” Robotica 23(2), 219 (2005).CrossRefGoogle Scholar
Nabavi, S. N., Akbarzadeh, A. and Enferadi, J., “Closed-Form Dynamic Formulation of a General 6-P US Robot,” J. Intell. Rob. Syst. 96(3–4), 317330 (2019).CrossRefGoogle Scholar
Koplik, J. and Leu, M., “Computer generation of robot dynamics equations and the related issues,” J. Rob. Syst. 3(3), 301319 (1986).Google Scholar
Liping, W., Huayang, X. and Liwen, G., “Kinematics and inverse dynamics analysis for a novel 3-PUU parallel mechanism,” Robotica 35(10), 20182035 (2017).CrossRefGoogle Scholar
Ojeda, J., Martínez-Reina, J. and Mayo, J., “The effect of kinematic constraints in the inverse dynamics problem in biomechanics,” Multibody Syst. Dyn. 37(3), 291309 (2016).CrossRefGoogle Scholar
Wei, H.-X., Wang, T.-M., Liu, M. and Xiao, J.-Y., “Inverse dynamic modeling and analysis of a new caterpillar robotic mechanism by Kane’s method,” Robotica 31(3), 493501 (2013).CrossRefGoogle Scholar
Zhao, Y. and Gao, F., “Inverse dynamics of the 6-dof out-parallel manipulator by means of the principle of virtual work,” Robotica 27(2), 259 (2009).CrossRefGoogle Scholar
González, F. and Kövecses, J., “Use of penalty formulations in dynamic simulation and analysis of redundantly constrained multibody systems,” Multibody Syst. Dyn. 29(1), 5776 (2013).CrossRefGoogle Scholar
Mo, J., Shao, Z.-F., Guan, L., Xie, F. and Tang, X., “Dynamic performance analysis of the X4 high-speed pick-and-place parallel robot,” Rob. Comput. Integr. Manuf. 46, 4857 (2017).CrossRefGoogle Scholar
Pappalardo, C. M. and Guida, D., “On the Lagrange multipliers of the intrinsic constraint equations of rigid multibody mechanical systems,” Archive of Applied Mechanics 88(3), 419451 (2018).CrossRefGoogle Scholar
Raoofian, A., Kamali, A. and Taghvaeipour, A., “Forward dynamic analysis of parallel robots using modified decoupled natural orthogonal complement method,” Mech. Mach. Theory 115, 197217 (2017).CrossRefGoogle Scholar
Yuan, W.-H. and Tsai, M.-S., “A novel approach for forward dynamic analysis of 3-PRS parallel manipulator with consideration of friction effect,” Rob. Comput. Integ. Manuf. 30(3), 315325 (2014).CrossRefGoogle Scholar
Arian, A., Danaei, B. and Tale Masouleh, M., “Kinematic and Dynamic Analyses of Tripteron, an Over-Constrained 3-DOF Translational Parallel Manipulator, through Newton-Euler Approach AUT,” J. Model. Simul. 50(1), 6170 (2018).Google Scholar
Cibicik, A. and Egeland, O., “Dynamic modelling and force analysis of a knuckle boom crane using screw theory,” Mech. Mach. Theory 133, 179194 (2019).CrossRefGoogle Scholar
Bi, Z. and Kang, B., “An inverse dynamic model of over-constrained parallel kinematic machine based on Newton–Euler formulation,” J. Dyn. Syst. Meas. Contr. 136(4), (2014).CrossRefGoogle Scholar
Gan, D., Dai, J. S., Dias, J. and Seneviratne, L., “Joint force decomposition and variation in unified inverse dynamics analysis of a metamorphic parallel mechanism,” Meccanica 51(7), 15831593 (2016).CrossRefGoogle Scholar
Khalil, W. and Ibrahim, O., “General solution for the dynamic modeling of parallel robots, J. Intell. Rob. Syst. 49(1), 1937 (2007).CrossRefGoogle Scholar
Roth, B., Screws, motors, and wrenches that cannot be bought in a hardware store In, Proc. Int. Symp. Robotics Research. pp. 679-693 (1984).Google Scholar
Pottmann, H. and Wallner, J., Computational line geometry (Springer Science & Business Media, 2009).CrossRefGoogle Scholar
Dai, J. S. and Sun, J., “Geometrical revelation of correlated characteristics of the ray and axis order of the Plücker coordinates in line geometry,” Mech. Machine Theory 153, 103983 (2020).CrossRefGoogle Scholar
Geike, T. and McPhee, J., “Inverse dynamic analysis of parallel manipulators with full mobility,” Mech. Mach. Theory 38(6), 549562 (2003).CrossRefGoogle Scholar
Gallardo-Alvarado, J., Aguilar-Nájera, C. R., Casique-Rosas, L., Rico-Martínez, J. M. and Islam, M. N., “Kinematics and dynamics of 2 (3-RPS) manipulators by means of screw theory and the principle of virtual work,” Mech. Mach. Theory 43(10), 12811294 (2008).CrossRefGoogle Scholar
Zhao, T., Geng, M., Chen, Y., Li, E. and Yang, J., “Kinematics and dynamics Hessian matrices of manipulators based on screw theory,” Chin. J. Mech. Eng. 28(2), 226235 (2015).CrossRefGoogle Scholar
Fan, S. and Fan, S., “An improved approach to the inverse dynamic analysis of parallel manipulators by a given virtual screw,” Adv. Rob. 32(16), 887902 (2018).CrossRefGoogle Scholar
Chai, X., Wang, M., Xu, L. and Ye, W., “Dynamic Modeling and Analysis of a 2PRU-UPR Parallel Robot Based on Screw Theory,” IEEE Access 8, 7886878878 (2020).CrossRefGoogle Scholar
Angeles, J. and Lee, S. K., “The formulation of dynamical equations of holonomic mechanical systems using a natural orthogonal complement, (1988).Google Scholar
Angeles, J., Fundamentals of Rigid-Body Mechanics (Springer, 2007).Google Scholar
Eskandary, P. K. and Angeles, J., “The dynamics of a parallel Schönflies-motion generator,” Mech. Mach. Theory 119, 119129 (2018).CrossRefGoogle Scholar
Taghvaeipour, A., Angeles, J. and Lessard, L., “Constraint-wrench analysis of robotic manipulators,” Multibody Syst. Dyn. 29(2), 139168 (2013).CrossRefGoogle Scholar
Ghaedrahmati, R., Raoofian, A., Kamali, A. and Taghvaeipour, A., “An enhanced inverse dynamic and joint force analysis of multibody systems using constraint matrices,” Multibody Syst. Dyn. 46(4), 329353 (2019).CrossRefGoogle Scholar
Angeles, C. T. J., “Rational Kinematics Springer, (1989).CrossRefGoogle Scholar
Tsai, L.-W., “The Jacobian analysis of a parallel maniuplator using the theory of reciprocal screws,” Digital Repository at University of maryLand, (1998).CrossRefGoogle Scholar
Dai, J. S., Huang, Z. and Lipkin, H., “Mobility of overconstrained parallel mechanisms, (2006).Google Scholar
Zhao, J., Li, B., Yang, X. and Yu, H., “Geometrical method to determine the reciprocal screws and applications to parallel manipulators,” Robotica 27(6), 929 (2009).Google Scholar
Raoofian, A., Taghvaeipour, A. and Kamali, A., “On the stiffness analysis of robotic manipulators and calculation of stiffness indices,” Mech. Mach. Theory 130, 382402 (2018).CrossRefGoogle Scholar
Dai, J. S. and Jones, J. R., “Null–space construction using cofactors from a screw–algebra context,” Proc. Royal Soc. London. Series A: Math. Phys. Eng. Sci. 458(2024), 18451866 (2002).CrossRefGoogle Scholar
Gosselin, C. and Angeles, J., “A global performance index for the kinematic optimization of robotic manipulators,” (1991).Google Scholar
Kövecses, J. and Ebrahimi, S., “Parameter analysis and normalization for the dynamics and design of multibody systems,” J. Comput. Nonlinear Dyn. 4(3), (2009).CrossRefGoogle Scholar
Chen, C., Peng, F., Yan, R., Li, Y., Wei, D., Fan, Z., Tang, X. and Zhu, Z., “Stiffness performance index based posture and feed orientation optimization in robotic milling process,” Rob. Comput. Integ. Manuf. 55, 2940 (2019).CrossRefGoogle Scholar
Taghvaeipour, A., Angeles, J. and Lessard, L., “On the elastostatic analysis of mechanical systems,” Mech. Mach. theory 58, 202216 (2012).CrossRefGoogle Scholar
Pennestrì, E., Valentini, P., Figliolini, G. and Angeles, J., “Dual Cayley–Klein parameters and Möbius transform: Theory and applications,” Mech. Mach. Theory 106, 5067 (2016).CrossRefGoogle Scholar