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This paper presents two ways for the minimization of joint reaction forces due to inertia forces (dynamic joint reaction forces) in a two degrees of freedom (2-DOF) planar serial manipulator. The first way is based on the optimal selection of the angular rotations laws of the manipulator links and the second one is by attaching counterweights to the manipulator links. The influence of the payload carrying by the manipulator on the dynamic joint reaction forces is also considered. The expressions for the joint reaction forces are obtained in a symbolic form by means of the Lagrange equations of motion. The inertial properties of the manipulator links are represented by dynamical equivalent systems of two point masses. The weighted sum of the root mean squares of the magnitudes of the dynamic joint reactions is used as an objective function. The effectiveness of the two ways mentioned is discussed. [Projekat Ministarstva nauke Republike Srbije, br. TR35006 i br. TR35038]

A two-stage optimization method for optimal dynamic design of planar mechanisms is presented in this paper. For dynamic balancing, minimization of the shaking force and the shaking moment is achieved by finding optimum mass distribution of mechanism links using the equimomental system of point-masses in the first stage of the optimization. In the second stage, their shapes are synthesized systematically by closed parametric curve, i.e. cubic B-spline curve corresponding to the optimum inertial parameters found in the first stage. The multi-objective optimization problem to minimize both the shaking force and the shaking moment is solved using evolutionary optimization algorithm – “Teaching-learning-based optimization (TLBO) algorithm”. The computational performance of TLBO algorithm is compared with another evolutionary optimization algorithm, i.e. genetic algorithm. [ABSTRACT FROM AUTHOR]

In this paper, a two stage optimization technique is presented for optimum design of planar slider-crank mechanism. The slidercrank mechanism needs to be dynamically balanced to reduce vibrations and noise in the engine and to improve the vehicle performance. For dynamic balancing, minimization of the shaking force and the shaking moment is achieved by finding optimum mass distribution of crank and connecting rod using the equimomental system of point-masses in the first stage of the optimization. In the second stage, their shapes are synthesized systematically by closed parametric curve, i.e., cubic B-spline curve corresponding to the optimum inertial parameters found in the first stage. The multi-objective optimization problem to minimize both the shaking force and the shaking moment is solved using Teaching-learning-based optimization algorithm (TLBO) and its computational performance is compared with Genetic algorithm (GA). [ABSTRACT FROM AUTHOR]

This paper presents a two stage optimization procedure for dynamic balancing of planar mechanisms and finding optimum link shapes. In the first stage, the shaking force and shaking moment are minimized by optimizing mass distribution of links using the equimomental system of point-masses for each link. Then for the optimum inertial parameters of the balanced mechanism, the optimum links shapes are synthesized systematically using closed parametric curve such as cubic B-spline in the second stage. The control points of cubic B-spline curve are taken as the design variables for link shape formation to minimize the percentage error in the resulting link inertia values. The constraints on design variables are defined for both symmetrical and non-symmetrical shapes in the optimization problem formulation. The proposed method of balancing and shape synthesis can be applied to any planar single and multiloop mechanism with revolute as well as prismatic joints. Its effectiveness is demonstrated by applying it to four-bar, five-bar, six-bar and slider-crank mechanisms. [ABSTRACT FROM AUTHOR]

This paper presents an optimization method to find link shapes for a dynamically balanced planar four-bar mechanism. The shaking force and shaking moment developed in the mechanism due to inertia are minimized by optimally distributing the link masses. The link shapes are then found using cubic B-spline curves and an optimization problem is formulated to minimize the percentage error in resulting links inertia values in which the control points of B-spline curve are taken as the design variables. The effectiveness of the proposed method is shown by applying it to a numerical problem available in the literature. [ABSTRACT FROM AUTHOR]

An optimization methodology is presented for design of serial-chain planar robots for minimizing torque at joints, when its endeffector is supposed to move on a prescribed path. In particular, the end-effector of the robot is allowed to move on a circular path. For the respective joint trajectories, the weighted sum of root mean square (RMS) of the actuating torques is minimized by the mass redistribution of the links. To achieve the goal, the DeNOC (Decoupled natural orthogonal complement) based dynamics was formulated by representing the rigid links as a set of rigidly connected point-masses known as equimomental system. The methodology is illustrated using a planar two-degree-of-freedom (DOF) robot with two revolute joints. [ABSTRACT FROM AUTHOR]

This paper presents an optimization technique to dynamically balance the planar mechanisms in which the shaking forces and shaking moments are minimized using the genetic algorithm (GA). A dynamically equivalent system of point-masses that represents each rigid link of a mechanism is developed to represent link's inertial properties. The shaking force and shaking moment are then expressed in terms of the point-mass parameters which are taken as the design variables. These design variables are brought into the optimization scheme to reduce the shaking force and shaking moment. This formulates the objective function which optimizes the mass distribution of each link. First, the problem is formulated as a single objective optimization problem for which the genetic algorithm produces better results as compared to the conventional optimization algorithm. The same problem is then formulated as a multi-objective optimization problem and multiple optimal solutions are created as a Pareto front by using the genetic algorithm. The masses and inertias of the optimized links are computed from the optimized design variables. The effectiveness of the proposed methodology is shown by applying it to a standard problem of four-bar planar mechanism available in the literature. [ABSTRACT FROM AUTHOR]

Abstract: This paper presents a new generic optimization technique for the balancing of the shaking force and shaking moment due to inertia forces in spatial mechanisms. For given dimensions and input speed of a mechanism, the inertia forces depend only upon the mass distribution of the moving links. The equimomental system of seven point-masses is introduced to represent the inertial properties of the links and to identify optimizing variables. The effectiveness of the proposed methodology is illustrated using a spatial RSSR mechanism. [Copyright &y& Elsevier]

Abstract: A general mathematical formulation of optimization problem for balancing of planar mechanisms is presented in this paper. The inertia properties of mechanisms are represented by dynamically equivalent systems, referred as equimomental systems, of point-masses to identify design variables and formulate constraints. A set of three equimomental point-masses for each link is proposed. In order to determine the shaking forces and the shaking moments, the dynamic equations of motion for mechanisms are formulated systematically in the parameters related to the equimomental point-masses. The formulation leads to an optimization scheme for the mass distribution to improve the dynamic performances of mechanisms. The method is illustrated with two examples. Balancing of combined shaking force and shaking moment shows a significant improvement in the dynamic performances compared to that of the original mechanisms. [Copyright &y& Elsevier]