Manipulator velocities and static forces

Robotic manipulators are mechanisms that are used to transmit motions and forces. Their kinematic and static properties are thus basic characteristics that must be analyzed when controlling them but also within the design phase. Such kinematic properties are the transmission of joint rates to the end-effector velocities. The dual property is the transformation of end-effector forces to joint forces. This requires adequate modeling of the manipulators, where serial and parallel manipulators must be distinguished. Special situations where these transformation properties change drastically are so-called singularities. In this chapter, the kinematic modeling is reviewed making use of recursive frame transformation. The velocity and force transformation relation is derived and explained for several manipulators, serial as well as parallel manipulators. The phenomenon of singularities is discussed, and the conditions for the existence of singularities are presented. The motion planning and control requires the solution of the inverse kinematic problem. This is also discussed in this paper. In particular, kinematic redundancy and redundant actuation are introduced, and the inverse problem discussed.