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Force balancing is a very important issue in mechanism design and has only recently been introduced to the designing step of robotic mechanisms. In creating the best robot design, the statical balancing plays a vital role because it reduces the required motor power. To get a simple and more-effective control system, elimination or significant reduction of the gravity load at a powered joint is an important one. With utilization of these objectives an optimization problem is formulated. The average force on the gripper in the working area is taken as an objective function. The design variables are lengths of the links, angles between them and stiffness of springs. This paper describes the use of conventional and evolutionary optimization techniques such as Newton's method (NM), conjugate gradient method (CGM), Genetic Algorithm (GA), Elitist Non-dominated Sorting Genetic Algorithm (NSGA-II) and differential evolution (DE) to solve the above problem. An industrial robot with 6-degree-of-freedom (6-DOF) (APR 20) is considered as a numerical example. The robot has a spring balancing system that has to be optimized. The existing optimization model is improved by adding two new variables. Also, a comprehensive user-friendly general-purpose software package has been developed using VC++ to obtain the optimal parameters using the proposed DE algorithm. The methods used in this article can be applied to find out solutions for a wide range of similar problems without further simplifications.

This paper addresses the static balancing of a 6-degree-of-freedom (6-DOF) industrial manipulator (APR 20). Static balancing is defined as the set of conditions on mechanism dimensional and inertial parameters which, when satisfied, ensure that the weight of the links does not produce any torque (or force) at the actuators for any configuration of the mechanism, under static conditions. Static balancing leads to considerable reduction in the actuator torques (or forces), which in turn allows the use of less powerful actuators and therefore leads to more efficient designs. Hence, the balancing conditions are very important in a context of design of robot mechanism. Static balancing means that the weight of the links does not produce any force at actuators for any configuration of the manipulator. When a robot is statically balanced, its potential energy is constant for all possible configurations. Two methods are studied in literature for the static balancing are using counterweights (CW) and using springs. The balancing by masses is due to added CW or due to link's mass redistribution. In case of balancing by springs, changes in the mass and inertia parameters of the robot mechanism is insignificant because the weight of the built-in springs or cylinders are very less compared to the link weight. This is the main advantage of the balancing by springs. In certain cases, combination of both spring balancing and mass balancing (especially mass redistribution of the links) may be better.

A new modified optimization model for the problem of finding suitable design variables for spring balancing mechanism of the industrial robot APR 20 is formulated and solved. In this paper, five new design optimization methods based on conventional and evolutionary algorithms are presented. Also, a comprehensive user-friendly general-purpose software package has been developed using VC++ to obtain the optimal parameters using the proposed DE algorithm. The proposed evolutionary algorithms (GA, NSGA-II and DE) show their superior nature while solving the problem. The proposed algorithms (GA, NSGA-II and DE) are having very little computational time than conventional techniques (NM, CGM). From Table 2, this paper concludes that the proposed DE technique is superior to others in terms of accuracy (gives better results than the other methods) and fastness (the computational time is 1/3rd of that of the other methods except NM). This work opens the door for further investigations on how nature-based methods can be used to solve complex problems. It is obvious that the method can also be used to optimize structures of robot mechanisms and many other design problems of robots can be solved in the same manner.