A robot manipulator is a spatial mechanism consisting essentially of a series of bodies, called "links", connected to each other at "joints". The joints can be of various types: revolute, rotary, planar, prismatic, telescopic or combinations of these. A serial connection of the links results in an open-chain manipulator. Closed-chain manipulators result from non-serial (or parallel) connections between links. Actuators at the joints of the manipulator provide power for motion. A robot is usually not designed for a very specific or repetitive task which can be done equally well by task-specific machines. Its strength lies in its ability to handle a range of tasks by virtue of being "re-programmable". Therefore, in addition to the mechanical hardware two other elements are integral to the description of a robot: sensors and control. With the advent of micro-electronics and digital computers the availability of sensors is ever increasing and the control is usually done by software executed by computers which also collect the sensory data. It is possible to model quite accurately, the dynamics of robot manipulators for purposes of control. However, for most practical robots the models are complex and numerically intensive to calculate in real-time. Traditional analyses of robot manipulators consider the whole mechanism to be rigid. Relaxation of the assumption of rigidity leads to further complication of the dynamics of the manipulator, leading to more difficulties in control. The overall motion of the manipulator is augmented by additional motion due to the dynamics of flexibility which must be considered. Sensing is also made more difficult. However, the ability to control robots with significant structural flexibilities, referred to as flexible robots in the rest of this thesis, influences robotics in many ways. It allows for consideration of new applications, observance of less conservative structural design and performance enhancements in certain classes of robotic tasks, which will be addressed in greater detail in the sections which follow.