Theory of Machines and Mechanisms is one of the main branches of science including many sub-branches such as biomechanics, human machine systems, computational kinematics, mechatronics, robotics, design methodology, dynamics of machinery, gearings and transmissions, cams and linkages, micro machines, nonlinear oscillations, reliability of machines and mechanisms etc. In this large area of interest, this study can be matched with the sub groups biomechanics, robotics, computational kinematics and design methodology. The main concern of the thesis is the biokinematics of the human arm. In the process of design, a suitable tool for the kinematics of human arm is investigated as quaternions along with examples. Moreover, the history of the formulas of Dof is presented as 38 equations with the unique key controlling parameters that are used in the design of new Cartesian and serial platform type robot manipulators. Structural syntheses of new manipulators are considered.Simple serial platform structural groups in subspace 8.3, and general space 8.6 are presented along with examples. Furthermore, type synthesis of human arm is accomplished with the new proposed parallel manipulator for the shoulder, elbow and wrist complex. Finally, computational kinematics of the serial human wrist manipulator and the geometrical kinematic analysis of the orientation platforms of the new parallel manipulator design for the human arm are accomplished.