This paper introduces the use of planar parallelogram linkages as generalized joints in a robot manipulator. The inverse kinematics for all possible manipulators formed from 3 parallelogram and 3 revolute joints are derived from the closure equations of an equivalent closed loop linkage. The internal displacement coordinates of the manipulator are obtained by solving a quadratic and an 8th degree polynomial equation, which results in up to 16 different configurations of the manipulator arm.