In this thesis, a theory for inverse dynamic analysis of general three dimensional mechanical systems is developed. Euler parameters are employed to specify rotations of rigid bodies of a mechanical system. Kinematic constraint equation of the system is formulated through mathematical description of joints and simple constraints. Equation of motion is derived using Lagrange multipliers. Positions, velocities, and accelerations of rigid bodies of a mechanical system at a given time are first obtained from kinematic analysis. The data are then substituted to the equation of motion of the system, to calculate Lagrange multipliers that are interpreted as required joint forces to drive the system as specified.
A computer program based on the theory is developed and validity of the theory is fully demonstrated through various example problems.
A theory for optimal path planning of mechanical systems is also developed, which is one of the most important application areas of inverse dynamics.
