**2. Stewart platform system**

180 Serial and Parallel Robot Manipulators – Kinematics, Dynamics, Control and Optimization

(a) (b) (c)

Fig. 2. Stewart (a) and Gough (b) original design (Bonev, 2003)

(Niesing, 2001; Merlet, 2006; Wikipedia)

developed (Hunt, 1983).

Fig. 1. Applications of the Stewart Platform: medical, manufacturing and flight simulator

(a) (b)

SP was not attracted attention during the first 15 years since the first invention. Then, Hunt indicated the advantages of parallel robots. After 1983, researchers realized their high load carrying capacity and high positioning ability of these robots. Researchers were then started to study a detailed analysis of these structures. The widely used structure of SP, where top platform is connected to base platform using 6 linear axis with universal joints, was then

It is a well known fact that the solution of the forward kinematics problem is easier than the inverse kinematics problem for serial robot manipulators. On the other hand, this situation is the just opposite for a parallel robot. Inverse kinematics problem of parallel robot can be expressed as follows: position vector and rotation matrix in Cartesian space is given, and asked to find length of each link in joint space. It is relatively easy to find the link lengths because the position of the connecting points and the position and orientation of the moving platform is known. On the other hand, in the forward kinematics problem, the rotation matrix and position vector of the moving platform is computed with given the link lengths. Forward kinematic of the SP is very difficult problem since it requires the solution of many The system components are two main bodies (top and base plates), six linear motors, controller, space mouse, accelerometer, gyroscope, laser interferometer, force/torque sensor, power supply, emergency stop circuit and interface board. They are shown in Figure 3.

Fig. 3. Stewart platform system

A simple emergency stop circuit was designed to protect the motors, when they move to out of the limits. This circuit controls the power supply which gives the energy to the motors

Position Control and Trajectory Tracking of the Stewart Platform 183

Another software component is the control desk (interface is shown in Figure 6) which allows downloading applications, doing experiments, easily creating graphical user

As can be seen from Figure 6, panel on the left side is called "Navigator" and it has four tabs: experiment, instrumentation, platform and test automation. All files written for

Empty Layout

Tool Window

Instruments Window

Fig. 5. Dspace toolbox and library

interface and data acquisition.

Navigator

Fig. 6. Control desk interface

based on the signal of hall-effect sensors on each motor. A switch-mode 150W power supply with inhibit input and EMI filter is used to supply required energy. Also, an interface board was designed between controller and motors.

The Dspace DS1103 real time controller is used to implement control algorithms. DS1103 is a rapid prototyping controller that developed for designing and analyzing complex and difficult control applications. It has various inputs and outputs such as digital, analog digital converter, digital analog converter, serial interface, can-bus, pulse width modulation (PWM) channels and encoders in order to be used lots of peripheral unit like actuators and sensors. DS1103 has a real time interface (RTI) that allows fully programmable from the Simulink® block diagram environment. A dspace toolbox will be added to Simulink® after installing RTI, so it can be configured all I/O graphically by using RTI. You can implement your control and signal processing algorithms on the board quickly and easily. A general DS1103 controller board system is shown in Figure 4. It consists of a DS1103 controller card in expansion box, CLP1103 input-output connector and led panel, DS817 link card and a computer.

Fig. 4. A general DS1103 set-up