Abstract
The spherical wrist robot arm is the most common type of industrial robot. This paper presents an efficient analytical computation procedure of its inverse kinematics. It is based on the decomposition of the inverse kinematic problem to two less complex problems; one concerns the robot arm basic structure and the other concerns its hand. The proposed computation procedure is used to obtain the inverse kinematic position models of two robot arms: one contains only revolute joints and the other contains both revolute and prismatic joints. The 1st and 2nd time derivatives of the obtained models give more accurate inverse kinematic velocity and acceleration models than numerical differentiation. These models are verified by simulation for two different trajectories. The obtained results demonstrate the effect of the proposed procedure on reducing the necessary computation time compared to other computation techniques.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Pieper, D.L., The kinematics of manipulators under computer control Stanford Artificial Intelligent Project, Memo AIM-72, Oct. (1968).
Paul, R., Robot Manipulators: Mathematics, Programing, and Control, MIT Press, Cambridge, Mass., (1981).
Paul, R., Shimano, B. and Mayer, G.E., Kinematic control equations for simple manipulators, IEEE Trans. System Man Cybernet. SMC-11(6), 757–763 (1981).
Renaud, M., Geometric and kinematic models of robot manipulators-calculation of the Jacobian matrix and its inverse, 11th ISIR Tokyo, pp. 757–763 (1981).
Benatic, M., Morasso, P. and Tagliasco, V., The inverse kinematic problem for anthropomorphic manipulators Arms, J. Dynamic Systems, Measurement and Control, Trans. ASME. 102, 110–113 (1982).
Featherstone, R., Position and velocity and transformations between robot end effector coordinates and joint angles, Int. J. Robotics Res. 2, No. 2, Summer (1983).
Gorla, B. and Renaud M., Modèles des robots manipulators application à leur commande Cepadues Editions, Toulose (1984).
Lee, C.S.G. and Ziegler, M., A geometric approach in solving the inverse kinematics of PUMA robots, IEEE Trans. Aerospace Electron. Systems AES20(6), 695–706 (1984).
Tsai, L.W. and Morgan, A.P., Solving the kinematics of most general six and five degree of freedom manipulators by continuous methods, ASME Paper 84-DET-20, Design Engineering Technical Conf., Cambridge, Mass. (1984).
Megahed, S., Contribution à la modelisation géometrique et dynamique des robots manipulateurs à structure de chaîne cinématique simpel ou complexe application à leur commade, Thése d'Etat, Université Paul Sabatier, Toulouse, France (1984).
Parkin, E.R., Inverse robot kinematics derived from planes of movements, Robotics AGE, 20–29 August (1985).
Megahed, S., Inverse kinematics of industrial robot manipulators using analytical approaches, Proc. 3rd Int. Conf. PEDAC, Alexandria, Egypt, Dec. 12–14, (1986).
Paul, R.P. and Zhang, H., Computationally effecient kinematics for manipulators with spherical wrists based on the homogeneous transformation representation, Int. J. Robotics Res. 5(2), 32–44 (1986).
Craig, J.J., Introduction to Robotics: Mechanics and Control, Addison Wesley, New York (1986).
Ersu, E. and Nungesser, D., A numerical solution of the general kinematic problem, IEEE Conf. Robotics, Atlanta, pp. 162–168 (1984).
Lumelsky, V.J., Iterative coordinate transformation procedure for one class of robots, IEEE Trans. Systems Man Cybernat. SMC14(3), 500–505 (1984).
Goldenberg, A.A. and Lawrence, D.L., A generalized solution to the inverse kinematics of robotics manipulators, J. Dynamic System, Measurement, and Control, Trans. ASME 107, 103–106 (1985).
Goldenberg, A.A., Benhabib, B. and Fenton, R.G., A complete generalized solution to the inverse kinematics of robots, IEEE J. Robotics Autom. RA-1(1), 14–20 (1985).
Angeles, J., On the numerical solution of the inverse kinematics problem, Int. J. Robotics Res. 4(2), 21–27 (1985).
Megahed, S., Inverse kinematics of simple chain robot manipulators using iterative numerical approaches, Proc. 3rd Int. Conf. PEDAC86, Alexandria, Egypt, Dec. 12–14 (1986).
Low, K.A. and Dobey, R.N., A computative study of generalized coordinates for solving the inverse kinematics problem of 6R robot manipulators, Int. J. Robotics Res. 5(4), 69–88 (1986).
Angeles, J., Iterative kinematic inversion of general five axis robot manipulators Int. J. Robotics Res. 7(3), 52–63 (1987).
Manseur, R. and Doty, K.L., A fast algorithm for inverse kinematic analysis of robot manipulators, Int. J. Robotics Res. 7(3), 52–63 (1988).
Castelain, J.M., Flamme, J.M., Gorla, B. and Renaud, M., Computation of the direct and inverse geometric and differential models of robot manipulators with the aid of the hyper-complex theory, Proc. 16th ISIR Brussels, Sept. 30 Oct. 2, (1986).
Denavit, J. and Hartenberg, R.S., A kinematic notation for lower-pair mechanisms based on matrices, J. Appl. Mech., 215–221, June (1955).
Megahed, S., Inverse kinematics of robot arms: problem formulation and data transformation, 3rd Int. Conf. PEDD, Ain Shams University, Faculty of Engineering, Cairo, Egypt, Dec. 27–29 (1990).
Hollerbach, J.M. and Sahar, G., Wrist partitioned inverse kinematic acceleration and manipulator dynamics, Int. J. Robotics Res. 2(4), (1985).
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Megahed, S.M. Inverse kinematics of spherical wrist robot arms: Analysis and simulation. J Intell Robot Syst 5, 211–227 (1992). https://doi.org/10.1007/BF00247418
Received:
Accepted:
Issue Date:
DOI: https://doi.org/10.1007/BF00247418