Date of Award


Degree Type


Degree Name

Doctor of Philosophy (PhD)


Mechanical Engineering


Professor Mohamed A. Dokainish


Professor William M. Mansour


This research develops a new methodology for the control of two link flexible arms. The methodology is referred to here as "Nonlinear Integrated Tabular" NIT Control. Starting with a new trajectory, the inverse kinematic problem is solved and adequate algorithms are presented to evaluate the commanding voltages to guarantee that the wrist point will track the desired trajectory. Continuous and discontinuous paths are tried with models which were developed to account for the flexibility in the joints and the flexibility in the links. Lagrange's equation and finite element formulation were used to construct realistic models. Computer simulations were conducted to assess the control qualities for tracking using NIT. The accuracy, smoothness as well as the levels of the command signals during tracking were quantified to serve as criteria to evaluate the quality of tracking.

A number of classical controls were developed and applied to the elbow arm to compare NIT with the current available approaches. A proportional plus derivative plus gravity, a feedback linearization as well as a VEE-MOD-VEE controllers were tried. It was shown that NIT compares well with the most successful conventional methods. In addition, it was found to offer simple, smooth, robust, computationally economic controls. NIT compares well with the majority of the conventional methods.

An experimental setup was constructed with the objectives of verifying the analytical predictions. It was built in a modular form to allow continuity of research in this area at McMaster's laboratories. Great care and long hours were spent in the design, fabrication, assembly, debugging of the hardware for the mechanical parts. The setup is referred to here as FLEXROD. The up-to-date technologies available today were implemented in the design of FLEXROD which include Harmonic Drives for speed reduction and transputers for the controller. Enormous efforts went into streamlining the software and in developing the interfaces between the sensory system and the controller. Experiments were conducted to validate the transient dynamics of the elbow arm when the motors are brought to a sudden stop by applying the brakes simultaneously. Reasonable agreement was found between the analysis and the experiment. The thesis is concluded with recommendations for future research in this area to implement and develop NIT using FLEXROD.

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