Motor control in primates relates to a system which is highly redundant from the mechanical point of view--redundancy coming from an imbalance between the set of independently controllable variables and the set of system variables. The consequence is the manifestation of a broad class of ill-posed problems, problems for which it is difficult to identify unique solutions. For example (i) the problem of determining the coordinated patterns of rotation of the arm joints for a planned trajectory of the hand; (ii) the problem of determining the distribution of muscle forces for a desired set of joint torques. Ill-posed problems, in general, require regularization methods which allow to spell acceptable, if not unique, solutions. In the case of the motor system, we propose that the basic regularization mechanism is provided by the potential fields generated by the elastic properties of muscles, according to an organizational principle that we call "Passive Motion Paradigm". The physiological basis of this hypothesis is reviewed and a "Kinematic Network" (K-net) model is proposed that expresses the kinematic transformations and the causal relations implied by elasticity. Moreover, it is shown how K-nets can be obtained from a kinematic "Body Model", in the context of a specific task. Two particularly significant results are: (i) the uniform treatment of closed as well as open kinematic chains, and (ii) the development of a new method for the automatic generation of kinematic equations with arbitrary topology. Moreover, the model is akin to the concept of "motor equivalence" in the sense that it provides families of motor equivalent trajectories parametrized by tunable motor impedances.