Dynamic modeling is a fundamental step in analyzing the movement of any mechanical system. Methods for dynamical modeling of constrained systems have been widely developed to improve the accuracy and minimize computational cost during simulations. The necessity to satisfy constraint equations as well as the equations of motion makes it more critical to use numerical techniques that are successful in decreasing the number of computational operations and numerical errors for complex dynamical systems. In this study, performance of a variant of Kane’s method compared to six different techniques based on the Lagrange’s equations is shown. To evaluate the performance of the mentioned methods, snake-like robot dynamics is considered and different aspects such as the number of the most time-consuming computational operations, constraint error, energy error, and CPU time assigned to each method are compared. The simulation results demonstrate the superiority of the variant of Kane’s method concerning the other ones.

With rapid development of methods for dynamic systems modeling, those with less computation effort are becoming increasingly attractive for different applications. This paper introduces a new form of Kane's equations expressed in the matrix notation. The proposed form can efficiently lead to equations of motion of multi-body dynamic systems particularly those exposed to large number of nonholonomic constraints. This approach can be used in a recursive manner resulting in governing equations with considerably less computational operations. In addition to classic equations of motion, an efficient matrix form of impulse Kane formulations is derived for systems exposed to impulsive forces.

In this study, we analyze the influence of passive joint viscous friction (PJVF) on modal space decoupling for a class of symmetric spatial parallel mechanisms (SSPM). The Jacobian matrix relating the platform movements to each passive joint velocity is first gained by vector analysis and the passive joint damping matrix is then derived by applying the Kane method. Next, an analytic formula index measuring the degree of coupling effects between the damping terms in the modal coordinates is proposed using classical modal analysis of dynamic equations in task space. Based on the index, a new optimal design method is found which establishes the kinematics parameters for minimizing the coupling degree of damping and achieves optimal fault tolerance for modal space decoupling when all struts have identical damping and stiffness coefficients in their axial directions. To illustrate the effectiveness of the theory, the new method was used to redesign two configurations of a specific manipulator.