Document Type


Date of Award

Winter 1-31-1994

Degree Name

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


Mechanical and Industrial Engineering

First Advisor

Zhiming Ji

Second Advisor

Nouri Levy

Third Advisor

Ian Sanford Fischer


This thesis deals with solving the problem of placing the base plate in an optimum position and orientation in a three dimensional space for the desired locations of the mobile end platform of a Stewart platform parallel manipulator.

First the workspace of the mobile plate is expressed as a function of the base plate position. Then the objective function is generated by summing the squared distances from the various desired locations of the mobile plate to the center of the platform's workspace. This function consists of six unknown variables which define the position and orientation of the base plate. A computer program based on the Downhill Simplex method in multidimensions has been used to obtain the values of the six variables for the minimum value of the function when the end platform is placed in the desired locations. These values of the variables have been used to calculate the optimum location of the base plate. HOOPS software has been used to graphically represent the parallel manipulator in its calculated optimum position and orientation in a 3-d space for the desired locations of the end platform which has to be specified by the user.