Inverse dynamics of hexapods using the natural orthogonal complement method

The hexapods under study are parallel mechanisms made of fixed-length legs, as opposed to conventional hexapods with extensible legs. The former are becoming popular in developing machine tools for high-speed machining applications. In this paper, the inverse dynamics of hexapods with fixed-length legs is analyzed using the natural orthogonal complement method. This analysis includes the mass of the moving platform as well as those of the legs. The leg masses become important for high-speed applications. In this development, the Newton-Euler formulation is used to model the dynamics of each individual body, including the moving platform and the legs. This is followed by assembling the individual dynamics equations to form the global dynamics equations. Based on the complete kinematics model developed in the paper, an explicit expression is derived for the natural orthogonal complement that effectively eliminates the constraint forces in the global dynamics equations. This leads to the inverse dynamics equations of the hexapods that can be used to compute required actuator forces for given motions. Simulations are provided to demonstrate the developed method.

[1]  Jorge Angeles,et al.  Dynamic Simulation of n-Axis Serial Robotic Manipulators Using a Natural Orthogonal Complement , 1988, Int. J. Robotics Res..

[2]  Amir Fijany,et al.  Parallel computation of manipulator inverse dynamics , 1991, J. Field Robotics.

[3]  Jorge Angeles,et al.  Kinematics and dynamics of a six-degree-of-freedom parallel manipulator with revolute legs , 1997, Robotica.

[4]  J. Angeles,et al.  The Formulation of Dynamical Equations of Holonomic Mechanical Systems Using a Natural Orthogonal Complement , 1988 .

[5]  Karl-Heinz Wurst,et al.  Systematic Design of Hexapods and other Parallel Link Systems , 1997 .

[6]  Clément Gosselin,et al.  Singularity analysis of closed-loop kinematic chains , 1990, IEEE Trans. Robotics Autom..

[7]  Leonard S. Haynes,et al.  On the dynamic model and kinematic analysis of a class of Stewart platforms , 1992, Robotics Auton. Syst..

[8]  Fengfeng Xi,et al.  Effect of dynamic balancing on four-bar linkage vibrations , 1997 .

[9]  L. Tsai.  Solving the Inverse Dynamics of a Stewart-Gough Manipulator by the Principle of Virtual Work , 2000 .

[10]  Hidenori Kimura,et al.  A New Parallel Algorithm for Inverse Dynamics , 1989, Int. J. Robotics Res..

[11]  Koichi Sugimoto,et al.  Kinematic and Dynamic Analysis of Parallel Manipulators by Means of Motor Algebra , 1987 .

[12]  Jorge Angeles,et al.  THE MODELLING OF HOLONOMIC MECHANICAL SYSTEMS USING A NATURAL ORTHOGONAL COMPLEMENT , 1989 .

[13]  E F Fichter,et al.  A Stewart Platform- Based Manipulator: General Theory and Practical Construction , 1986 .

[14]  John C. Ziegert,et al.  Fundamental Comparison of the Use of Serial and Parallel Kinematics for Machines Tools , 1999 .

[15]  D. C. H. Yang,et al.  Inverse dynamic analysis and simulation of a platform type of robot , 1988, J. Field Robotics.

[16]  J. Angeles,et al.  Dynamics of Nonholonomic Mechanical Systems Using a Natural Orthogonal Complement , 1991 .