## 1 Introduction  
If we compare parallel manipulators (PM) with serial manipulators, we observe that parallel manipulators have some interesting advantages, such as a higher stiffness all over the workspace (WS), better load/weight ratio and lower inertia. Nevertheless, parallel manipulators have also some disadvantages--more complex kinematics and dynamics and also more complex and smaller workspace. In the last few years, parallel manipulators have been studied and used for applications where high stiffness, high speed and/or very good accuracy are required. Geometric parameters have a pronounced effect on these performance criteria of the parallel manipulators. Thus, the geometrical optimization of parallel manipulators is essential in order to obtain the desired performance in a particular application. Some of the possible performance criteria include design for best position accuracy, design to obtain the biggest possible workspace and design for optimum velocity, stiffness, force, dexterity or manipulability all over the workspace. As [PERSON] et al. [1] explained, depending on the application, certain performance criteria are more important than others. Thus, one of the first steps is to define the application of the parallel manipulator we want to design and identify how the different parameters of the manipulator affect the performance for that specific application. Performance requirements of parallel manipulators may be antagonistic to one another, as [PERSON] et al. [2] highlighted. If so, we can define an _appropriate design_ that does not optimize a single function but ensures that the manipulator satisfies all the desired requirements. Since small workspace is one of the biggest drawbacks of parallel manipulators, many authors have optimized different parallel manipulators to obtain a desired workspace. [PERSON] [3,4] presented a numerical method to obtain the geometries of a Gough-type PMwith its workspace containing a predefined one. [PERSON] et al. [5] and [PERSON] et al. [6] described different methods to obtain the parameters of a DELTA PM for a specific workspace. [PERSON] et al. [7] proposed an analytical approach to obtain the actuated joint stroke of a 6-PSS parallel manipulator for a desired cylindrical workspace and given orientation capability. [PERSON] et al. [8] presented a new PM with redundant actuation, the 2 UPR-2 PRU PM, and its optimal design that considered a good transmission workspace. In 2018, [PERSON] et al. [9] designed and analysed a new seven degree of freedom (DOF) parallel manipulator with foldable mobile platform. They chose the kinematic parameters in order to obtain a large workspace with homogeneous performance in the different DOFs. Parameters such as dexterity or stiffness have also been used to optimize parallel manipulators. [PERSON] and [PERSON] [10] maximized the local dexterity of a family of 6-DOF Stewart platform parallel manipulators. [PERSON] and [PERSON] [11] introduced the _global conditioning index_ and used it to optimize the global dexterity of 3-DOF planar and spatial parallel manipulators. [PERSON] [12] proposed a dimensional and topological optimization method of manipulators to obtain a desired stiffness. [PERSON] [13] introduced a new hybrid parallel manipulator and optimized it to provide a better dexterity and singularity-free workspace characteristics. Other works, such as the one presented by [PERSON] et al. [14] used a multi-objective optimization method for the 3-RPS parallel manipulator that considered the global conditioning index, the global stiffness index and the workspace volume. Recently, [PERSON] et al. [15] analysed a compliant parallel manipulator and developed the design synthesis by considering the stiffness, the global condition number and the norm of the actuator forces. They used an evolutionary algorithm to perform a simultaneous optimization of these three parameters. One parameter that has received less attention in the literature is the dynamic performance.