The effects of design parameters on the workspace of a 3-DOF U[P.bar]U micro parallel robot.

Stab, Sergiu ; Maties, Vistrian ; Balan, Radu 等

Abstract: In this paper a workspace analysis for a three-degree of freedom parallel micro robot is outlined by using optimality criterion of workspace and numerical aspects. We proposed a numerical procedure for determining and evaluating the workspace of the U[P.bar]U robot architecture. The analysis and algorithm can be used as a design tool to select dimensions, actuators and joints in order to maximize the workspace and improve stiffness within the workspace. A program was created in MATLAB for workspace analysis of 3 DOF parallel robots.

Key words: workspace, UPU, parallel robot, 3DOF.

1. INTRODUCTION

In the literature, various methods to determine workspace of a parallel robot have been proposed using geometric or numerical approaches. Parallel robots have become a large area of interest in the field of robotics. Parallel robots generally have larger load capacities, faster and more accurate motions and a larger stiffness throughout their workspace as compared to the serial ones (Hesselbach, 2004).

Early investigations of robot workspace were reported by (Merlet, 1995). Other works that have dealt with robot workspace are reported by (Agrawal, 1990), Ceccarelli [11]. Agrawal determined the workspace of in-parallel manipulator system using a different concept namely, when a point is at its workspace boundary, it does not have a velocity component along the outward normal to the boundary.

Configurations are determined in which the velocity of the end-effector satisfies this property. In (Stan, 2003) was presented a genetic algorithm approach for multi-criteria optimization of PKM.

The workspace of a robot is defined as the set of all end-effector configurations which can be reached by some choice of joint coordinates.

As the reachable locations of an end-effector are dependent on its orientation, a complete representation of the workspace should be embedded in a 6-dimensional workspace for which there is no possible graphical illustration; only subsets of the workspace may therefore be represented.

2. THREE-DOF UPU MICRO PARALLEL ROBOT

A spatial parallel robot is formed when two or more spatial kinematic chains act together on a common rigid platform. One of the most common spatial parallel architecture is UPU.

The spatial micro 3 DOF parallel robot is shown in Fig.1. This structure is also known as UPU robot. Since mobility of this micro parallel robot is three, three actuators are required to control this robot. The 3-UPU mechanism features platform and base interconnected by three serial lunematic chains of type UPU, where U stands for universal joint, and the prismatic pair P is actuated. 3-UPU mechanism recently attracted attention for its elegant and symmetric topology.

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3. WORKSPACE ANALYSIS

The knowledge of the workspace of a 3 DOF micro parallel robot is very important in planning a dexterous manipulation task. The workspace is one of the most important kinematic properties of robots, even by practical viewpoint because of its impact on robot design.

In this section, the workspace of the proposed robot will be discussed systematically. Here, we propose an approach to compute and visualize the workspace of a 3 DOF micro parallel robot. Micro parallel robots are good candidates for microminiaturization into a microdevice. It is very important to analyze the area and the shape of workspace for parameters given robot in the context of industrial application. The main disadvantage of parallel robots is their small workspace in comparison to serial arms of similar size. Despite the advantages of parallel manipulators there are certain disadvantages to be encountered such as complicated kinematics and dynamics, many singular configurations, and poor workspace availability.

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Resolution of the latter is very important for any manipulator design. If we restrict ourselves to a 3-DOF parallel robot (a U[P.bar]U parallel robot for example) we will find that the link lengths limit the workspace. On the other hand, there will necessarily be a design limitation of some sort on the link lengths. Also one must have a compact design which is capable of full manoeuvring. The workspace is primarily limited by the boundary of solvability of inverse kinematics. Then the workspace is limited by the reachable extent of drives and joints, occurrence of singularities and by the link and platform collisions.Analysis, visualization of workspace is an important aspect of performance analysis. A numerical algorithm to generate reachable workspace of parallel manipulators is introduced. This section presents the methodology to determine the workspace of the 3 DOF micro parallel robot. It consists of several MATLAB scripts and functions used for workspace analysis and kinematics of the parallel robot. A friendly user interface was developed using the MATLAB-GUI (graphical user interface). Several dialog boxes guide the user through the complete process. In the followings are presented the workspace of the U[P.bar]U parallel robot for different values of diameter of the circle for the lower platform, d.

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This graphical user interface (Fig. 2) can be a valuable and effective tool for the workspace analysis and the kinematics of the parallel robots. The designer can enhance the performance of his design using the results given by the presented graphical user interface.

4. CONCLUSION

In this paper a workspace analysis for a three-degree of freedom parallel micro robot was outlined by using optimality criterion of workspace and numerical aspects. We proposed a numerical procedure for determining and evaluating the workspace of the UPU robot architecture. The analysis and algorithm can be used as a design tool to select dimensions, actuators and joints in order to maximize the workspace and improve stiffness within the workspace.

5. REFERENCES

J. Hesselbach, H. Kerle, M. Krefft, N. Plitea, (2004) "The Assesment of Parallel Mechanical Structures for Machines Taking Account of their Operational Purposes". In: Proc. of the 11th World Congress in Mechanism and Machine Science-IFToMM 11, Tianjin, China.

S. Stan, Diplomarbeit, (2003), Analyse und Optimierung der strukturellen Abmessungen von Werkzeugmaschinen mit Parallelstruktur, IWF-TU Braunschweig, Germany.

J. P. Merlet. (1995), "Determination of the orientation workspace of parallel manipulators". Journal of intelligent and robotic systems, 13:143-160.

SK. Agrawal, (1990) "Workspace boundaries of in-parallel manipulator systems". Int. J. Robotics Automat, 6(3) 281-290.

M. Cecarelli, (1995) "A synthesis algorithm for three-revolute manipulators by using an algebraic formulation of workspace boundary". ASME J. Mech. Des. 1995; 117(2(A)): 298-302.

Jason J. Lee and Sun-Lai Chang, "On the kinematics of the UPS wrist for real time control", DBVol. 45, 22nd ASME Biennial Mechanisms Conference, Robotics, Spatial Mechanisms, and Mechanical Sysrems. Scorndale, Arizona, pp. 305-312, 1992.