## 1 Introduction
This parameter is usually antagonistic to the overall stiffness of the manipulator, so both parameters are typically considered together. [PERSON] et al. [16] proposed a 5-DOF PM for machining purposes, and they proposed a Driving System Parameter optimization to improve its dynamic performance. [PERSON] et al. [17] designed a multi-objective optimization method for spherical PMs that evaluates the kinematics and the stiffness of the manipulator. In 2020, [PERSON] et al. [18] derived the 22 kinematically identical manipulators--identical kinematics but different constraints--of the 2-RPU-UPR parallel manipulator and optimized them in terms of motion/force transmission indices. In 2016, [PERSON] et al. [19] presented the design optimization and control of compliant actuation arrangements for articulated robots in order to improve energy efficiency. Recently, they applied this method in [20] to optimize three design parameters of a leg with serial and parallel compliant actuation in order to minimize the electrical power consumption. In order to optimize the robot geometry and pose for a given set of points, [PERSON] et al. [21] proposed a dual multi-objective novel methodology that combines dimensional synthesis and a path planning algorithm. They validated this method with a four degree of freedom robot for high-precision laser operations in aero-engines. The most common techniques used to solve the optimization problem are the objective-function based optimal design and using performance charts. In the objective-function technique, we first have to define an objective function and then apply an optimization algorithm to find the optimal result. This technique needs an initial value to be defined, which is not trivial. Moreover, it is time-consuming, and it is very difficult to find an optimum solution for multiple criteria due to the antagonism of performance criteria. The performance chart technique shows the relationship between a performance index and related design parameters. This relationship is presented for all the performance indexes and design parameters, which allows us to observe how antagonistic the chosen criteria are. The optimum result is fuzzier when we apply the performance chart than when we apply the objective-function technique. However, the performance chart provides more than one solution to a design problem, so we can say that it is a more flexible technique. This allows the designer to adjust the optimum result taking the design conditions into account. The biggest drawback of this technique is that the value of each parameter of the manipulator can be between zero and infinite, so it is very important to pre-define a range of values. [PERSON] and [PERSON] [22] presented the parameter-finiteness normalization method to find a solution to the parameter infinity problem. They presented a new design methodology for mechanisms with less than five linear parameters. The main advantages of this method are that one performance criterion corresponds to a chart, that the optimal solution can consider multi-objective functions and guarantees the optimal solution and that it provides all the possible optimal solutions. In 2015, [PERSON] et al. [23] presented an optimization method for reconfigurable manipulators. This method allows obtaining the best position of the grasping points in the mobile platform in order to obtain the most regular workspace. They applied the method to the reconfigurable manipualtor PARAGRIP and proposed to measure the regularity of the workspace by measuring the size of the biggest sphere that fits in the useful workspace. In this work, we propose two optimization algorithms based on grid search that consider the size and regularity of the workspace. The first algorithm obtains the geometric parameters combination that results in the biggest and most regular workspace. It is based on the idea proposed by [PERSON] et al.