Abstract: In general, the kinematics design problems include two types: synthesis of mechanism and inverse of robot. In fact, when we deal with the design problems, the results/outputs usually are given/desired but the inputs are unknown/to be found. People must understand how to control/determine the input variables to satisfy the results/outputs. This paper systematically presents these two types of solution based on transformation matrix and Homotopy continuation method for general kinematics design problems except for mechanism and robot. The kinematic equations, which include displacement, velocity and acceleration relationships, are derived by 4x4 homogeneous transformation matrix method. Also these equations can be solved by Homotopy continuation method when these equations are non-linear.