This thesis presents a method for determining range of body motion for a walking machine with feet fixed on the ground. The darkling beetle was selected as the sample subject in this study. A closed form inverse kinematic solution is used to determine if a point in space is within range of body motion. An algorithm for tracing workspace boundary is also presented. The software, developed in Microsoft QuickC, has three main parts: (1) a module for searching the workspace contours and recording the contour points, (2) a plotting program for presentation of the workspace on the screen, (3) a module to determine ranges of roll, pitch and yaw for specified foot positions. The plotting program shows four views of the workspace, including front, top, and side views, and user specified axonometric projection. Body range of motion for a representative set of foot positions is presented and analyzed. Results are presented for normal resting height (10mm) and for 8mm and 12mm heights. Body range of motion for feet positioned for the alternating tripod gait is also presented. Ranges of roll, pitch and yaw have been determined and are discussed. / Graduation date: 1991

This thesis examines the influence on range-of-motion of beetle body of changes in leg segment parameters. From beetle's leg orientation, influence of the following leg segment parameters are investigated: coxa length, coxa twist and body-coxa joint. Kinematic equations are derived for legs of the beetle. Roots of quartic polynomials obtained while solving the kinematic equations are found by using the Bairstow (1966) numerical method. Inverse kinematic solutions are obtained for each leg and used to determine whether a point is within the body range of motion or not. An algorithm developed by Mason (1957) and Cordray (1957) for tracing closed boundaries is used to find ranges of motion of the body and feet. Changes in body range of motion caused by alteration in leg segment parameters are complex and not easy to explain. Similarities between changes in body range of motion and foot range of motion are observed. A great deal more work is necessary to fully understand the importance of observed changes. / Graduation date: 1992