Abstract: Based on the signed distance function from point to surface, this paper defined the signed distance function from surface to surface, analyzed the first and second differential properties and derived its 2nd Taylor expansion. Then by using the theories of signed distance function, 1st and 2nd free motions were presented in order to describe rigid body B motion with respect to multiplefinger A1,A2,…Ak and the 1st and 2nd free motion have the feature of coordinate invariance. Based on the 1st and 2nd free motion, a new method was presented to analyze the immobility of multiplefinger grasps. Lastly, the simulation result of four fingers’ immobile grasp at a tetrahedral shows the validity of the method.