Abstract
This paper presents the kinematic analysis and trajectory planning for a six-degrees-of-freedom end-effector whose design is based on the Stewart platform mechanism. The end-effector is composed of two platforms and six linear actuators driven by stepper motors. A spring-loaded platform is used to provide passive compliance to the end-effector during a part assembly. A closed-form solution is derived for the inverse kinematic transformation and a computationally effective numerical solution is obtained for the forward kinematic transformation using the Newton-Raphson method. Three trajectory planning schemes, two for fine motion and one for gross motion are developed. Experimental results of tracking various test paths are presented.
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References
Stewart, D., A platform with six degrees of freedom, Proc. Institute of Mechanical Engineering 180, Part 1, No. 5, 371–386 (1965–1966).
Dieudonne, J.E. et al., An actuator extension transformation for a motion simulator and an inverse transformation applying Newton-Raphson's method, NASA Technical Report D-7067, 1972.
Hoffman, R. and McKinnon, M.C., Vibration modes of an aircraft simulator motion system, Proc. Fifth World Congress for the Theory of Machines and Mechanisms, 1979, pp. 603–606.
McCallion, H. and Truong, P.D., The analysis of a six-degree-of-freedom work station for mechanised assembly, Proc. Fifth World Congress for the Theory of Machines and Mechanisms, 1979, pp. 611–616.
Hunt, K.H., Kinematic Geometry of Mechanisms, Pxford University Press, London, 1978.
Sugimoto, K. and Duffy, J., Application of linear algebra to screw systems, Mech. Mach. Theory 17(1), 73–83 (1982).
Hunt, K.H., Structural kinematics of in-parallel-actuated robot arms, Trans. ASME, J. Mech. Transmis. Automat. Design 105, 705–712 (1983).
Premack, T. et al., Design and implementation of a compliant robot with force feedback and strategy planning software, NASA Technical Memorandum 86111, 1984.
Nguyen, C.C., Pooran, F.J. and Premack, T., Control of robot manipulator compliance, in M.Jamshidi, J.Y.S.Luh and M.Shahinpoor (eds), Recent Trends in Robotics: Modeling, Control and Education, North-Holland, New York, 1986, pp. 237–242.
Yang, D.C. and Lee, T.W., Feasibility study of a platform type of robotic manipulators from a kinematic viewpoint, Trans. ASME J. Mech. Transmis. and Automat. Design 106, 191–198 (1984).
Mohammed, M.G. and Duffy, J., A direct determination of the instantaneous kinematics of fully parallel robotic manipulators, ASME J. Mech. Transmis. Automat. Design 107, 226–229 (1985).
Fichter, E.F., A Stewart platform-based manipulator: General theory and practical construction, Internat. J. Robotics Res., 157–182 (Summer 1986).
Sugimoto, K., Kinematic and dynamic analysis of parallel manipulators by means of motor algebra, ASME J. Mech. Transmis. Automat. Design 108, 1–5 (1986).
Lee, K.M., Chao, A. and Shah, D.K., A three degrees of freedom in-parallel actuated manipulator, Proc. IASTED Int. Conf., 1986, pp. 134–138.
Rees-Jones, J., Cross coordinate control of robotic manipulators, in Proc. Internat. Workshop on Nuclear Robotic Technologies and Applications, Present and Future, University of Lancaster, UK, 29 June–1 July, 1987.
Behi, F., Kinematic analysis for a six-degree-of-freedom 3-PRPS parallel mechanism, IEEE J. Robotics Automat. 5(5), 561–565, 1988.
Sharon, A., Hogan, N. and Hardt, D., High-bandwidth force regulation and inertia reduction using a macro/micro manipulator system, Proc. IEEE Internat. Conf. on Robotics and Automation, Philadelphia, PA, April 1988, pp. 261–266.
Sugimoto, K., Computational scheme for dynamic analysis of parallel manipulators, in Trends and Developments in Mechanisms, Machines, and Robotics-1988, ASME Proc. 20th Biennial Mechanisms Conf., 1988.
Kerr, D.R., Analysis, properties, and design of a Stewart-platform transducer, in Trends and Developments in Mechanisms, Machines, and Robotics-1988, ASME Proc. 20th Biennial Mechanisms Conf., 1988.
Nguyen, C.C. and Pooran, F.J., Adaptive force/position control of robot manipulators with closed-kinematic chain mechanism, in M.Jamshidi et al. (eds), Robotics and Manufacturing: Recent Trends in Research, Education, and Application, ASME Press, New York, 1988, pp. 177–186.
Griffis, M. and Duffy, J., A forward displacement analysis of a class of Stewart platforms, J. Robotic Systems 6, 703–720 (1989).
Nguyen, C.C. and Pooran, F.J., Kinematic analysis and workspace determination of a 6 DOF CKCM robot end-effectors, J. Mech. Working Technol. 20, 283–294 (1989).
Nguyen, C.C. and Pooran, F.J., Dynamical analysis of 6 DOF CKCM robot end-effector for dual-arm telerobot systems, J. Robotics and Autonom. Systems 5, 377–394 (1989).
Nanua, P., Waldron, K.J. and Murthy, V., Direct kinematic solution of a Stewart platform, IEEE Trans. Robotics Automat. 6(4), 438–444 (1990).
Nguyen, C.C. and Pooran, F.J., Learning-based control of a closed-kinematic chain robot end-effector performing repetitive tasks, Internat. J. Microcomputer Appl. 9(1), 9–15 (1990).
Nguyen, C.C., Antrazi, S. and Zhou, Z-L., Trajectory planning and kinematic control of a Stewart platform-based manipulator, Proc. 5th Internat. Conf. CAD/CAM Robotics and Factories of the Future, Norfolk, Virginia, December 1990.
Nguyen, C.C., Antrazi, S., Zhou, Z-L. and Campbell Jr., C.E., Experimental study of motion control and trajectory planning for a Stewart platform robot manipulator, Proc. IEEE Internat. Conf. Robotics and Automation, Sacramento, California, April 1991.
Press, W.H. et al., Numerical recipes in C: The Art of Scientific Computing, Cambridge University Press, 1988.
Fu, K.S. et al., Robotics: Control, Sensing, Vision, and Intelligence, McGraw-Hill, New York, 1987.
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Nguyen, C.C., Antrazi, S.S., Park, JY. et al. Trajectory planning and control of a Stewart platform-based end-effector with passive compliance for part assembly. J Intell Robot Syst 6, 263–281 (1992). https://doi.org/10.1007/BF00248019
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DOI: https://doi.org/10.1007/BF00248019