Document Type

Thesis

Date of Award

1-31-1993

Degree Name

Master of Science in Mechanical Engineering - (M.S.)

Department

Mechanical and Industrial Engineering

First Advisor

Zhiming Ji

Second Advisor

Rong-Yaw Chen

Third Advisor

Avraham Harnoy

Abstract

A Stewart platform is a fully parallel, six-degree-of-freedom manipulator mechanism. A platform manipulator has a fixed platform acting as base, a mobile platform on which end-effector is mounted, and in-parallel kinematics chains (legs) between the two platforms. Although some direct position kinematics solutions for Stewart platforms of simplified geometry have been represented, to the best of our knowledge, no close-form direct kinematics solution for the general Stewart platform is available yet.

A common feature of six-degree-of-freedom Stewart platform of simplified geometry is the use of pairs of concentric ball joints. Due to inevitable manufacturing and assembly errors, practically there are no perfect concentric ball joints. This thesis presents an efficient method for solving the forward kinematics of this class of general Stewart platforms. The approach described in this thesis first finds an initial solution by approximating the original platform with a platform of simplified geometry, then improve the solution with a Jacobian based method. A numerical example is used to illustrate the method.

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