The forward and reverse solutions of a manipulator with six joints are expanded up to second order in the 24 joint param eters. Assuming that the 24 errors of the 24 joint parameters are independent of the setting of the six controllable joint parameters, if suffices to triangulate the six coordinates (three translational, three rotational) of the end-effector and sub tract the ideal position computed from the forward solution of the ideal error-free robot. This provides 24 equations for 24 unknowns. Calibration compensation consists of correcting the six controllable joint parameters by six controllable ad justments so that the effect of the 24 errors is compensated for.
Get full access to this article
View all access options for this article.
References
1.
Ball, R.S.1900. The theory of screws. Cambridge: Cambridge University Press.
2.
Book, W.J.1984. Recursive lagrangian dynamics of flexible manipulator arms. Int. J. Robotics Res.3(3):87-101.
3.
Brady, M., Hollerbach, J.M., Johnson, T.L., Lozano-Pérez, T., and Mason, M.T.1982. Robot motion: Planning and control. Cambridge: MIT Press.
4.
Duelen, G., Kirchhoff, U., and Held, J.1984 (May 21-23, Pittsburgh, Pa.). The inverse kinematic problem in real-time application. Computer based factory automation. SME 11th Conf. on Production Research and Technology: 393-400.
5.
Duffy, J.1980. Analysis of mechanisms and robot manipulators. London: Arnold; New York: Wiley.
6.
Featherstone, R.1983. The calculation of robot dynamics using articulated body inertias. Int. J. Robotics Res.2(1):13-30.
7.
Featherstone, R.1984 (April 10-11, Cambridge, Mass.). Spatial notation: A tool for robot dynamics. Institute of Measurement and Control Symposium on "Robotics-Dynamics, Control and Advanced Programming. "
8.
Hollerbach, J.M.1980. A recursive lagrangian formulation of manipulator dynamics and a comparative study of dynamics formulation complexity. IEEE Trans. Sys., Man Cyber. SMC-10(11):739-736.
9.
Hunt, K.H.1984. Mechanisms—research directions in kinematics and geometry. J. Mech., Trans. Automat. Design106(3):262-263.
10.
Kumar, A., and Waldron, K.J.1981. Numerical plotting of positioning accuracy of manipulators . Mechanism Mach. Theory16(4):361-368.
11.
Luh, J.Y.S., Walker, M.W., and Paul, R.P.C.1980. On-line computational scheme for mechanical manipulators . J. Dyn. Sys. Meas. Control102(1):69-76.
12.
Megahed, S., and Renaud, M.1982 (June 9-11, Paris). Minimization of the computation time necessary for the dynamic control of robot manipulators . 12th Int. Symp. on Industrial Robots. Bedford: IFS, pp. 469-478.
13.
Mooring, B.W.1983 (August 7-11, Chicago). The effect of joint axis misalignment on robot positioning accuracy. Proc. 1983 ASME Int. Conf. on Computers in Engineering. New York: ASME, pp. 151-155.
14.
Paul, R.P.1981. Robot manipulators: Mathematics, programming, and control . Cambridge: MIT Press.
15.
Rooney, J.1978. A comparison of representations of general spatial screw displacement. Environment and PlanningB5(1):45-88.
16.
Sugimoto, K., and Duffy, J.1982. Application of linear algebra to screw systems. Mechanism Mach. Theory17(1):73-83.
17.
Sugimoto, K.1984. Determination of joint velocities of robots by using screws . J. Mech., Trans. Automat. Design106(2):222-227.
18.
Mises, R.1924. Motorrechnung, ein neues Hilfsmittel der Mechanik. ZAMM4(2):155-181, (3):193-213.
19.
Walker, M.W., and Orin, D.E.1982. Efficient dynamic computer simulation of robotic mechanisms. J. Dyn. Sys., Meas. Control. 104(3):205-211.
20.
Whitney, D.E., DeFazio, T.L., Gustavson, R.E., Rourke, J.M., Seltzer, D.S., Edsall, A.C., Lozinski, C.A., and Kenwood, G.J.1984. (May 21-23, Pittsburgh, Pa.). Short- and long-term robot feedback: Multi-axis sensing, control and updating. Computer based factory automation. 11th Conf. on Production Research and Technology: 147-152.
21.
Whitney, D.E., and Lozinski, C.A.1984. (Las Vegas, Nev.). Industrial robot calibration methods and results. Proc. 1984 ASME Conf. on Computers in Engineering.
22.
Wu, Chi-haur1984. A kinematic CAD tool for the design and control of a robot manipulator. Int. J. Robotics Res.3(1):58-67.
