The optimum kinematic design of a spatial nine-degree-of-freedom parallel manipulator

This paper considers the kinematic optimization of a parallel manipulator actuated in redundant form, using a numeric conditioning of the Jacobian matrix. The kinematic model proposed by Zanganeh and Angeles (1994) consists of nine prismatic in-parallel actuators, i.e., three actuators, called external legs, connect the moving platform directly to the base platform by spherical joints, and the six actuators, termed the upper internal and the lower internal legs, are coupled in pairs by three concentric spherical joints at the internal point. First, the end effector velocity problem is solved, and then the identification of a neutral configuration of manipulator is developed. Finally, the platform geometry parameters of the manipulator are formulated, and solved as an optimization problem.

[1]  J. Uhlig.  C. Forsythe and C. B. Moler, Computer Solution of Linear Algebraic Systems. (Series in Automatic Computation) XI + 148 S. Englewood Cliffs, N.J. 1967. Prentice-Hall, Inc. Preis geb. 54 s. net , 1972 .

[2]  John J. Craig,et al.  Articulated hands: Force control and kinematic issues , 1981 .

[3]  J.-P. Merlet.  The importance of optimal design for parallel structures , 1999 .

[4]  G. Forsythe,et al.  Computer solution of linear algebraic systems , 1969 .

[5]  C. Gosselin,et al.  The optimum kinematic design of a spherical three-degree-of-freedom parallel manipulator , 1988 .

[6]  Jorge Angeles,et al.  Instantaneous kinematics and design of a novel redundant parallel manipulator , 1994, Proceedings of the 1994 IEEE International Conference on Robotics and Automation.

[7]  G. Forsythe,et al.  Computer solution of linear algebraic systems , 1969 .

[8]  Joseph Duffy,et al.  Hybrid Twist and Wrench Control for a Robotic Manipulator , 1988 .

[9]  Åke Björck,et al.  Numerical Methods , 1995, Handbook of Marine Craft Hydrodynamics and Motion Control.

[10]  Jorge Angeles,et al.  Mobility and position analyses of a novel redundant parallel manipulator , 1994, Proceedings of the 1994 IEEE International Conference on Robotics and Automation.

[11]  Ou Ma.  Mechanical analysis of parallel manipulators with simulation, design, and control applications , 1991 .

[12]  Tsuneo Yoshikawa,et al.  Manipulability of Robotic Mechanisms , 1985 .

[13]  Richard P. Paul,et al.  Kinematics of Robot Wrists , 1983 .