In this paper, we answer two interleaved questions. The first one is, having a redundant serial manipulator with a given cyclic task, how can we benefit simultaneously from both natural dynamics modification (NDM) and kinematic redundancy resolution to reduce the actuators' torque? Here, the NDM is done by devising parallel nonlinear monoarticular compliances (MACs), which span one joint, and nonlinear biarticular compliances (BACs), which pass over two joints. We take advantage of kinematic redundancy to exploit the robot's natural dynamics. The second question is how do kinematic redundancy resolution and the NDM interact to minimize the cost? To answer these questions, we cast the problem of simultaneous modification and exploitation of natural dynamics into a constrained multiobjective optimization problem. We show that the set of optimal compliances has an analytical solution as a parametric function of joint trajectories. Accordingly, we study how the components of cost function affect the profile of optimal compliant elements. The proposed method is implemented on a simulated planar 3-DoF manipulator and a simulated nonplanar 4-DoF manipulator for three different tasks. The results shed light on how kinematic redundancy resolution influences efficiency of using MACs and BACs and, consequently, increases attainable gains from the NDM. Moreover, analysis of the results specifies the roles of mono- and BACs and especially explains the reason behind the particular importance of having BACs to reduce the actuation cost.

In this paper, we propose a new method for implementing a rotational nonlinear spring with user defined profile, based on the combination of a linear spring with a nonlinear transmission mechanism. The proposed structure consists of a non-circular cam, a roller which moves along outer circumference of the cam, and a stretched translational linear spring which is connected between center of the cam and center of the roller. We obtain a set of differential equations to design shape of the cam for any given torque-angle profile. Also, it will be shown that profiles with both positive and negative values can be implemented by the proposed method. At last, the cam of some popular nonlinear springs are designed, including constant, cubic, hyperbolic tangent and sinusoidal springs.