First Advisor

Dongik Joo

Date of Publication


Document Type


Degree Name

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


Mechanical Engineering




Robots -- Error detection and recovery -- Mathematical models, Robots -- Error detection and recovery -- Computer simulation, Manipulators (Mechanism) -- Mathematical models, Manipulators (Mechanism) -- Computer simulation, Computer algorithms



Physical Description

1 online resource (3, x, 71 p.)


The growing need in industrial applications of high-performance robots has led to designs of lightweight robot arms. However the light-weight robot arm introduces accuracy and vibration problems. The classical robot design and control method based on the rigid body assumption is no longer satisfactory for the light-weight manipulators. The effects of flexibility of light-weight manipulators have been an active research area in recent years. A new approach to correct the quasi-static position and orientation error of the end-effector of a manipulator with flexible links is studied in this project. In this approach, strain gages are used to monitor the elastic reactions of the flexible links due to the weight of the manipulator and the payload in real time, the errors are then compensated on-line by a control algorithm. Although this approach is designed to work for general loading conditions, only the bending deflection in a plane is investigated in detail. It is found that a minimum of two strain gages per link are needed to monitor the deflection of a robot arm subjected to bending. A mathematical model relating the deflections and strains is developed using Castigliano's theorem of least work. The parameters of the governing equations are obtained using the identification method. With the identification method, the geometric details of the robot arms and the carrying load need not be known. The deflections monitored by strain gages are fed back to the kinematic model of the manipulator to find the position and orientation of the end-effector of the manipulator. A control algorithm is developed to compensate the deflections. The inverse kinematics that includes deflections as variables is solved in closed form. If the deflections at target position are known, this inverse kinematics will generate the exact joint command for the flexible manipulator. However the deflections of the robot arms at the target position are unknown ahead of time, the current deflections at each sampling time are used to predict the deflections at target position and the joint command is modified until the required accuracy is obtained. An experiment is set up to verify the mathematical model relating the strains to the deflections. The results of the experiment show good agreement with the model. The compensation control algorithm is first simulated in a computer program. The simulation also shows good convergence. An experimental manipulator with two flexible links is built to prove this approach. The experimental results show that this compensation control improves the position accuracy of the flexible manipulator significantly. The following are the brief advantages of this approach: the deflections can be monitored without measuring the payload directly and without the detailed knowledge of link geometry~ the manipulator calibrates itself with minimum human intervention; the compensation control algorithm can be easily integrated with the existing uncompensated rigid-body algorithm~ it is inexpensive and practical for implementation to manipulators installed in workplaces.


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