Abstract: The dimensional synthesis,problem of robot manipulatcrs is investigated in thispaper.A system of nonlinear constraint equations relating the position of hand havi-ng extreme distance to the positions of joints for robot are derived in rectangular co-ordinate system.In the paper a mathematical model for optimal synthesis is establis-hed.An objective function based on position err or and the design variables which canbe arbitrarily choseh in optimization are presented.Presented algorithm can be appledto determine the kinematic parameters of robot in accordance with a series of pointson a given boundary curve.It is pointed out that the algorithm is very effective andpractical.Finally,a numerical example is given to illustrate the algorithm.