Latest Papers

ASME Journal of Mechanisms and Robotics

  • Dynamics of Mobile Manipulators Using Dual Quaternion Algebra
    on September 14, 2022 at 12:00 am

    AbstractThis article presents two approaches to obtain the dynamical equations of mobile manipulators using dual quaternion algebra. The first one is based on a general recursive Newton–Euler formulation and uses twists and wrenches, which are propagated through high-level algebraic operations and works for any type of joints and arbitrary parameterizations. The second approach is based on Gauss’s Principle of Least Constraint (GPLC) and includes arbitrary equality constraints. In addition to showing the connections of GPLC with Gibbs–Appell and Kane’s equations, we use it to model a nonholonomic mobile manipulator. Our current formulations are more general than their counterparts in the state of the art, although GPLC is more computationally expensive, and simulation results show that they are as accurate as the classic recursive Newton–Euler algorithm.

Design of Torque-Compensated Mechanical Systems With Two Connected Identical Slider-Crank Mechanisms


Balancing the torque of mechanisms designed to minimize the fluctuation of input shaft torque is an effective means of improving their dynamic performance. There are several ways of solving the problem: optimizing the distribution of the moving mass of the original mechanism; cam sub-systems that displace the balancing mass; cam-spring mechanisms; flywheels driven by noncircular gears; adding articulated dyads, linkages or redundant drivers. This paper addresses the problem of input torque compensation with the optimal connection of two identical slider-crank mechanisms. The acceleration and deceleration phases of the links of the slide-crank mechanism obviously change periodically, causing torque to fluctuate at the input shaft. The problem is how to connect two mechanisms in order to reduce the input torque. This is done by minimizing the root-mean-square value of the input torque of the combined linkages. Two schemes are considered: slider-crank mechanisms with sliders moving on the same side, and on opposite sides. The prime value of this study is that it proposes an analytically tractable solution for identifying the general dynamic properties of mechanisms. Based on the ratio of link lengths, the precise relations for optimal connection of identical slider-crank mechanisms, i.e., a connection that produces the minimum root-mean-square values of the input torque, are developed. The numerical simulations illustrate the efficiency of the suggested approach. Observations show that the best solutions from the point of view of input torque minimization are obtained for the value of the coupling angle of two mechanisms around 90 deg.

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