Stiffness and Compliance of Kinematic Chains in Motion

The main aim of this thesis is the analysis of bioinspired kinematic chains controllable both in position and compliance (or stiffness) from a static and a dynamic point of view. In motion control theory, the redundancy of muscles, with respect to the number of degrees of freedom in a typical biomechanical system, permits the formulation of several control strategies. In this work the Feldman quadratic muscular model, proposing a direct connection between the magnitude and the frequency of sub-cortical electrical stimuli and muscular co-activation, is adopted. Two new indicators, the Dynamic Stiffness and Compliance Operators, are defined in a mathematical way by the use of functional analysis. These new indicators allow a theoretical and practical study of the performance of a chain during collisions or under external perturbations. The Dynamic Stiffness Operators can be useful in the treatment of many mechanical problems, as, for example, the estimation of the force generated by the system when it commits an error in terms of its trajectory, fundamental in breakable object manipulation. Instead, the Dynamic Compliance Operator, measuring the deviation from a given trajectory in presence of external perturbations, is defined as the inverse of the Stiffness Operator and is very more complex to calculate explicitly. In order to perform this calculation many mathematical instruments are used. Finally the mathematical theory developed in the thesis is applied to the design of electroactive polymer fiber bundles driven by bioinspired control variables to implement pseudomuscular actuators devoted to the realization of biomimetic movements.