This paper proposes a computational model for different aspects of trajectory formation, from point-to-point movements to handwriting. The proposed model is based on a mechanism of composition of basic curve elements (strokes) which separates the spatial and the temporal aspects of trajectory formation. At the same time, the model suggests a method for storing and describing arm movements, as a list of stroke descriptors. Experimental trajectories were digitized and analyzed with regard to several types of movements: i) point-to-point trajectories, ii) closed trajectories, iii) trajectories with inflection points, iv) spiral-like trajectories, v) handwritten trajectories. Velocity and curvature profiles were computed for the trajectories and the model was fitted to the data. The implications of the model and its "credibility" in the general context of motor control are discussed.

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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.

Experimental results presented in the literature suggest that humans use a position control strategy to indirectly control force rather than direct force control. Modeling the muscle-tendon system as a third-order linear model, we provide an explanation of why an indirect force control strategy is preferred. We analyzed a third-order muscle system and verified that it is required for a faithful representation of muscle-tendon mechanics, especially when investigating critical damping conditions. We provided numerical examples using biomechanical properties of muscles and tendons reported in the literature. We demonstrated that at maximum isotonic contraction, for muscle and tendon stiffness within physiologically compatible ranges, a third-order muscle-tendon system can be under-damped. Over-damping occurs for values of the damping coefficient included within a finite interval defined by two separate critical limits (such interval is a semiinfinite region in second-order models). An increase in damping beyond the larger critical value would lead the system to mechanical instability. We proved the existence of a theoretical threshold for the ratio between tendon and muscle stiffness above which critical damping can never be achieved; thus resulting in an oscillatory free response of the system, independently of the value of the damping. Under such condition, combined with high muscle activation, oscillation of the system can be compensated only by active control.