Computational kinematics of general Stewart platform

Date of Completion

January 2005


Engineering, Mechanical




This dissertation addresses the kinematics, redundancy resolution and control methods for Stewart platform and algorithms for mechanism design and optimization. ^ In this dissertation, techniques are developed to support Jacobian analysis and position analysis for kinematics of Stewart platform. Especially, a numerical method for finding all the solutions of the forward position analysis problem for the most general Stewart platform is presented. This method is based on the polynomial continuation method. However, it constructs start system and the homotopy based on physical design rather than mathematical equations. It has superior efficiency since it eliminates all of the extraneous paths before the solution tracking procedure starts. This method is further generalized as a "Continuous Design Transmutation Method" for solving problems in engineering analysis and design, which involve searching solutions of a system of polynomial equations. ^ To overcome deficiencies of Stewart platform, redundancy schema are suggested in this work. The kinematic constraint equations and system Jacobian for redundant Stewart platform are developed. The global optimal resolutions of joint rates are formulated and solved as a problem of the calculus of variations. The results show that significant improvement can be achieved by introducing and optimizing the redundant DOF. ^ A new manipulation method for controlling compliant motion of a Stewart platform is presented. In this work, the force and position variables are packed into one set of "motion feedback" by replacing the force errors with virtual motion quantities. The joint inputs are adjusted based on this combined feed back package. Since only the Jacobian of inverse kinematics is used in the control scheme, the computational complexity is reduced. The applications of this method are demonstrated in simulation experiments. ^ At last, a formulation and numerical method for design and optimization of the profile of cutting blades is presented. It is shown that the front line curvature of a cutting blade is related with the cutting force and input force or torque in the form of a first-order differential equation. The mechanics in the cutting process can be improved by adjusting the curvature of the rotary blade according to the solution of the differential equation. ^