**Abstract**

This document presents the design of a digital PID control for a Stewart-Gough platform, delimited by six degrees of freedom (DoF) that allow the final effector to have displacement in the XYZ axes and rotation with warpage, pitch, and yaw restrictions. It includes the study and resolution of the direct and inverse kinematics of the platform, as well as the workspace described by the final effector and its corresponding simulation of movements and joints to study extreme points and possible singularities. From the definition of characteristics, the CAD design generated from the generalized mathematical model of the public domain, and the general selection of materials for the construction of the functional prototype, a study of applied forces is generated to observe the points with stress concentrators, the safety factor, and possible deformations. The estimation of the sampling period for the selection of the microcontroller and an approximate definition of the response time are also considered. The development of this prototype and its documentation are proposed as didactic material for the study, design, and control of parallel mechanisms.

**Keywords:** Stewart-Gough platform, PID control, parallel robots, inverse kinematics, CAD design

### **1. Introduction**

When talking about industrial robotics, one of the first associated thoughts is about the serial robots that are highly applicable to this field; however, parallel robots also have a great importance and range of applications in this environment. Among its most important characteristics, its high load/power ratio is distinguished. In the case of the Stewart-Gough platform, this characteristic lies in its possibility of distributing the load in approximately six equal parts, whereby the total load capacity of the parallel robot approximates six times the load capacity of each actuator individually.

The Stewart platform is a parallel type manipulator that involves a configuration of six degrees of freedom, and each degree of freedom corresponds to an actuator. The six actuators can be linear or angular and join the bottom of the robot, which has no mobility, called a base with the part that does have mobility, the final effector. Due to this configuration, the Stewart-Gough platform has high rigidity, which can be translated into greater precision.

The final effector is the most interesting part of the robot, since its position and even orientation are the characteristics that determine if the robot is able to meet the precision necessary to implement and satisfy a need, whether industrial, educational, research, etc. It can have different applications, for example, orientation of satellites, flight simulators, and shakers (or also called agitators that are part of the chemistry laboratory instruments), among others.

This document explains the design, construction, and implementation of a discrete PID control to a Stewart-Gough platform.
