Degree Name

Doctor of Philosophy


Department of Mechanical Engineering


This thesis deals with automated symbolic derivation of dynamic equations of motion and applications to determine dynamic load carrying capacity (DLCC) for flexible manipulators.

Firstly, a recursive Lagrangian assumed mode method was modified to model the manipulator by including joint flexibility and dynamics of the load and actuator joint dynamics. Secondly, the thesis presents the development of a symbolic derivation and dynamic simulation package for flexible manipulators using a PC-based symbolic language MATHEMATICA® . The package, which takes full advantages of the symbolic language, incorporates automatic simplification, numerical solution, and graphic representation in a user-friendly environment and is applicable to multilink flexible manipulators. A case study of a two-link flexible manipulator is presented and the results are subsequently applied to determine dynamic load carrying capacity for the flexible manipulator. Simulation results are compared with different approaches as well as the rigid case. Techniques for overcoming computer memory limitation, simplifying intermediate derivation, and improving efficiency of equation generation are also discussed.

The thesis then presents the formulation and numerical solution of the Dynamic Load Carrying Capacity (DLCC) problem of flexible manipulators. For manipulators under the rigid body assumption, the major limiting factor in determining the maximum allowable load (mass and mass moment of inertia) for a prescribed dynamic trajectory (positions, velocities and accelerations) is the joint actuator capacity, while the flexibility inevitably exhibited by relatively light weight robots or by robots operating at a higher speed dictates the need for an additional constraint to be imposed for tasks requiring precision tracking, that is, the allowable deformation at end effector. The deflection equations are coupled with robot kinematics to solve for the generalized coordinates. A strategy to determine the DLCC subject to both constraints mentioned above is formulated where the end effector deflection constraint is specified in terms of a series of spherical bounds with a radius equal to the allowable deformation. A general computational procedure for the multiple-link case given arbitrary trajectories is laid out in detail. The results further confirm the necessity of the dual constraints and indicate which constraint is more critical for a given robot and trajectory depends on the required tracking accuracy.

Finally, the thesis considers a new formulation as well as numerical solution for the problem of finding a point-to-point trajectory with maximum load carrying capacities for flexible manipulators. The method of Iterative Linear Programming (ILP) and the computaional procedure for computing such optimal trajectory are developed. The procedure allows synthesizing point-to-point robot motions with a specified time and maximum load carrying capacity. The algorithm takes into account the complete dynamics equation and generalized coordinates and actuator constraints. To evaluate the performance of the proposed method, simulation tests are carried out.