This paper describes the application of our theory for kinematic synthesis of articulated systems with contact task specifications to the simultaneous synthesis of mechanical fingers for coordinated movements. The contact direction and curvature constraints between the fingers and a body are transformed into conditions on the velocity and acceleration of certain points using the task geometry. The addition of requirements on the accelerations allows for a more accurate definition of the tasks in the vicinity of the specified positions, thus considering the local motions of the fingertips and a grasped object and accounts for the smoothness of motion on the design level. The position and higher order motion specifications provide position, velocity and acceleration synthesis equations, which can be solved in order for the fingers to obtain the desired coordinated task. It should be noted that the use of kinematic synthesis as a first step in the design of the multi-fingered robotic hands has been applied to individual fingers, however a technique for doing this simultaneously for multiple fingers does not exist.