The development of hexapod kinematic structure.

Poppeova, Viera ; Uricek, Juraj ; Zahoransky, Robert 等

1 INTRODUCTION

Parallel kinematics structure (PKS) is mechanism with closed kinematical chain, which consists of the base, platform and at least two reciprocally independent leading legs. Parallel links (struts, legs) are joining between the base and the movable platform. Motion of the platform relatively to the base is controlled by a change of linear or angular parameters of several prismatic joints or legs acting in parallel system (kinematic chains). The most common configuration comprises six active legs and it is named Hexapod. These legs are realized as the linear actuators, most frequently by electromechanical cylinders. In this case the movable platform has six degrees of freedom (DOF)--moving in three linear directions and three angular directions independently or in any combination (Merlet, 2000; O'Connor, 1998).

This type of structure has been known for long time. Around 1800 the mathematician Cauchy studied the stiffness of the so-called "articulated octahedron" (Knoflicek & Kolibal, 2000). More recently in 1949, Gough used similar mechanism for the test of tyres. Then later in 1965, these mechanisms rediscovered and used very widely in the flight simulator by an engineer called D. Stewart. Since that time, any parallel linkage mechanisms are referred to as "Stewart platforms", although Gough discovered this mechanism before him.

The main fields where are applied this kind of mechanisms, are design of machine tools and robotics. Although the speed, accuracy, and flexibility of conventional machine tools have improved over the years, the basic design remains unchanged-tool and workpiece are still constrained to move along linear axes. Now, this long-standing configuration has competition from machines based on parallel or hybrid kinematics.

Since with the hexapod design the only forces on the machine's structure are tension and compression, it is less susceptible to bending than a conventional machine design.

Starting with the public presentation of the first parallel kinematic machines (PKM) on the IMTS fair in Chicago (1994), extensive research has been conducted university laboratories as well as in machine tool industry. During the last decade, more than 200 different parallel mechanisms have been built, mostly as prototypes or academic studies.

A first parallel mechanism device was used in a robotics assembly cell by McCallion in 1979. Then, Parallel manipulators have been under increasing development over the last few decades, so they are considered to be attractive alternative to the serial linkage devices, such as the conventional robotics arms (Marek, 2006; Chren, 2007).

2 DESIGN OF THE SCHOOL HEXAPOD

The school hexapod and its control system were developed at the University of Zilina at Department of Machining and Automation in last few years.

Mechanical construction

The mechanical construction consists of base, platform and six identical linear actuators with trapez system screw-nut. For the conection to the base and also to the platform are used the cardan joints (Fig. 1).

Parameters of school hexapod:

* DOF : 6[degrees]

* Dimensions a x b x c : 700 x 600 x 600 mm

* Weight: 40 kg

* Max. angle of platform rotation Ux, Uy, Uz: 30[degrees]

* Max. operating space X-axis, Y-axis: -50 to +50 mm

* Max. operating space Z-axis : 0 to +100mm

Mathematical model

To fully describe the position and orientation of the movable platform in the workspace, six coordinates are needed. Three of them are positional displacements that define the actual position of tool centre point (TCP) fixed on the platform with respect to global coordinate system (fixed with base). The other three coordinates are angular displacements that define the orientation of the platform. We define generalised Cartesian space coordinates p, whose elements are the six variables chosen to describe the position and orientation of the platform, as p = f (x, y, z, [phi], [theta], [psi]).

The position of the platform frame is specified with respect to the base frame by a vector [[bar.P].sub.p] = (x, y, z), which gives the coordinates of point [P.sub.0] with respect to the base frame. The orientation of the platform frame is described with respect to the base frame by a matrix of rotation.

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3 SIMULATION SOFTWARE

The simulation software for school hexapod was created in the same time than the engineering design of mechanical structure. It was designed in environment of program language Delphi 7 with the support of library Open GL.

Computer simulation of school hexapod structures is used for system study on its mathematical model. System's action is defined as relation system for transformation of parameters from imput and status space to parameters in its output and status space. It is possible to use the data from simulation software for control of real hexapod (Fig. 3).

For mechanism simulation is important information about dimensions and forms its kinematic chains and joins, presentations of position its elements.

4 CONTROL SYSTEM

It was designed one of possible architecture of control system for designed PKS. Proposed scheme of control system is based on master PC (on this PC is running a simulation/control software), which generates the data necessary for control systems of each of drives. The communication between the master PC and each control moduls is realized by converter USB--RS232 (Fig. 4).

The control system of drives is designed for DC motor with feedback included incremental or Hall sensor. DC motor is controled by the pulse width modulation (PWM). Current protection is realized by comparator, which swich off the H-bridge in case when become overload (Fig. 5).

5 CONCLUSION

PKS development is short-run compared with long-run machinery development with serial kinematic structure.

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Whereupon it is possible to expect, that in the future will arise more and more projects supporting PKS research (Knoflicek & Kolibal, 2000, Marek, 2006).

At University of Zilina (Slovakia) was designed school hexapod with six degrees of freedom. There were designed hexapod mechanical elements, inverse kinematic analyse, 3D model, simulation software and hexapod control system.

Designed hexapod can be used as teaching aid for better understanding of parallel structure behavior and also as basis for next development in the area PKS.

Acknowledgement

The article was made under support of Slovak Grant Agency KEGA--project No 3/4098/06.

6 REFERENCES

Chren, O. (2007). A kinematical variation of the tricept, ERIN2007 International Conference, pp. 14-17, ISBN 978-80-227-2636-8, STU Bratislava, April 2007, Slovakia

Knoflicek, R. & Kolibal, Z. (2000). Morphological analyse of Industrial Robots Design (in Czech), VIENALA Kosice, ISBN 80-88922-27-5, Kosice, Slovakia

Marek, J. (2006). Machining centres with unconventional structure (in Czech). MM Prumyslove spektrum, specialedition - Design of CNC machine tool. September 2006, Praha, MM publishing, p. 234-243, pp. 282, ISSN 1212-2572

Merlet, J.-P. (2000). Parallel robots, Kluwer Academic Publisher, Dordrecht

O'Connor, R. (1998). Design News--Inverted struts improve hexapod rigidity. Accessed: 1998-02-16. Available from: http://www.designnews.com/article/CA112337.html

www.parallemic.org

www-sop.inria.fr/members/Jean-Pierre.Merlet//merlet_eng.html