الفهرس 
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Abstract
The main objective of this work is to study both the singularity of 3-dof planar
Parallel manipulators with three identical legs , and the stiffness for these
Manipulators.In planar motion, only prismatic and revolute joints can be considered. there are different architectures can occur, two of them [rrr’rpr]
Are examined in systematic manner using the screw theory .
Since the kinemati can elysis and velocity equations are derived by using screw
Theory,a considerable attention is paid to explaining the application of the application of the
Theory of screws in the plane including a short review a bout it .once these Velocity equations are set up, an exhaustive stud yon the various types of Singularities of these manipulatiors is performed.
The singularity of such planar Manipulators is studied for both non- redundant and redundant planar parallel Manipulators, and all possible cases of configurations are considered
A kinematic analysis of redundant parallel manipulators is presented giving a clear and distinct definition of all types of redundancy in addition, the same
two architectures are investigated by introducing redundancy in the same
manner using screw theory. It is proved that redundancy has agreat benefit to overcome the singutar configurations of parallel manipulators.