טכניון מכון טכנולוגי לישראל
הטכניון מכון טכנולוגי לישראל - בית הספר ללימודי מוסמכים  
M.Sc Thesis
M.Sc StudentGross Asaf
SubjectAnalysis of Dynamic Jumping Motion of a Robotic Leg
DepartmentDepartment of Mechanical Engineering
Supervisor Professor Yizhar Or
Full Thesis text - in Hebrew Full thesis text - Hebrew Version


Abstract

Jumping is a form of dynamic motion that allows the robot to overcome large obstacles and travel in rough terrain. The dynamics of jumping motion has been studied in several areas of research such as: Sport science and biomechanics, Animal studies and Robotics and control.

Although this kind of motion has been investigated in many different studies, in the papers examined as part of the literature review of this work, the parameters affecting the jumping locomotion are hidden and therefore, in those studies, the influence of these parameters' on jumping performance has not been explicitly analyzed.

The purpose of this study is to develop a series of simple models of a robotic jumper, with an increasing degree of complexity, so that in each model the effect of the parameters on the jumping dynamics is analyzed, and optimization of the jumping performance is proposed.

First this research considers a jumper model with two masses connected by a single prismatic joint which is actuated by a constant force. The prismatic joint is extending until it reaches a mechanical stop. This instantaneous stop induces an impact on the jumper and results in its detachment from the ground. The analysis was done for horizontal jumps as well as for vertical jumps, an analysis of the governing equations is performed to determine the optimal mass ratio and Optimal tilt angle which results maximal jumping height and horizontal distance.

For the horizontal jumper an analysis was preformed to include the slippage effect and an optimal tilt angle as a function of the friction coefficient was found.

Second the research discusses a jumper model with two masses connected by two rotary joints. This analysis was also performed for a vertical and horizontal jump and the horizontal distance was also calculated to include the slippage effect. In this model the Height and the horizontal distance of the jumper's center of mass is optimized. Combined numeric and analytic investigation of this model was performed assuming constant angular velocities. In order to find the optimal jumping distance, three independent parameters are discretized and the horizontal jumping distance is calculated as a three-dimensional matrix which depends on these parameters, then the globally maximal value in this matrix is found under equality and inequality constraints. In addition, this optimal solution is refined by using MATLAB's built-in procedure for constrained optimization. Minimal angular velocities required for contact detachment and the optimal configuration at detachment are found.