## 1 Introduction
There are many different types of geometrical interpretations of the Stewart platform, but the main objective of this paper is geometry optimization of the Stewart platform with rotary actuators, as shown in Figure 2. It has six pairs of upper and lower levers (together called legs), and the movement of the upper platform relative to the base is achieved by rotating the lower lever around an axis going through one end of a lever. This is the revolute joint between the base and a lower lever controlled by an electric motor. The upper and lower levers are connected with universal or spherical joints, which connect the upper lever and platform. This is why this type is also called 6-RUS, in accordance with the types of joints. Figure 1: Closed kinematic chain. The contribution of this paper is significant as it provides solutions to both inverse and forward kinematics problems for the rotary Stewart platform, besides the geometrical definition of the mechanism and algorithm for its optimization. To control the position and orientation of the platform, the part of the simulator that connects the base and platform (leg) needs to have an actuator. Some of the other geometrical types use six levers with variable lengths (linear or prismatic actuators) or six pairs of two levers, of which one lever is fixed but has a variable length. The most critical design aspects of the mechanism besides the types of actuators are spatial configuration (locations of connections) and the type of connections (joints). A design solution based on rotary actuators, in this case, electric motors with proper gearboxes, is adopted due to its simplicity in terms of simulation, production, and maintenance. If the servo motor with servo drive is not cost-effective, an induction motor or asynchronous motor can be controlled using a variable-frequency drive (VFD) and both products are standardized and widely available. The current angle of the shaft can be measured with an encoder or potentiometer. The mechanism with this type of actuator is the simplest one to scale down and test on a smaller model. Even before investing in the first prototype, kinematics and control algorithms can be physically tested. After selecting the type of actuator and spatial configuration, the remaining part of the simulator design is choosing values of predefined geometrical parameters that fully define the mechanism with all constraints. Due to many different combinations and their interrelated influence on the simulator performance, it is challenging to find optimal values for these parameters. In this case, with many parameters, often some optimization algorithms must be employed to get sufficiently good results in the desired time. For problems like this, the optimization algorithms are often numerical and do not provide the solution in the closed form. These algorithms are traditionally iterative. Constrained minimization problems can be solved with minimization of the fitness function by successive approaching within a sequence of calculations. There are already reasonable efforts in employing the genetic algorithm [28; 29; 30] for optimization of this kind of problem. It is suitable because there are many local minima, and it is not easy to find a global one. Brute force and exhaustive algorithms are not chosen in this case because of the computational power and time necessary for optimization. There are also more recent evolutionary and bio-inspired metaheuristic algorithms that can be used for this kind of problem, such as the ones described in [31; 32; 33]. The implementation of the fitness function defines the goal of optimization. Many performance indicators can be considered in this case while calculating fitness functions, such as the maximum feasible orientation of the platform, the volume of workspace, needed joint movements, manipulability, dexterity, singularities, and physical interference between segments. This paper proposes novel constraints, performance indica  
Figure 2: Stewart platform with rotary actuators.