Kinematic chain and structure behavior analysis for second joint of "RRR" type robot in order to increase its positioning accuracy.

Munteanu, Gabriel ; Ghiorghe, Adrian

1. INTRODUCTION

The goal of the present work is to analyze the behavior of the timing belt transmission within the second rotational joint as part of the kinematic chain within the mechanical system of RRR robot. Such analyses (Stanciu et al., 1999); (Kanarachos & Spentzas, 2004) were previously made for similar robot architectures using older techniques or virtual instruments.

Currently new improved software instruments are available, as: Ansys, LMS Virtual Lab, Nastran, modules integrated in Solid Works or Catia (Ghionea et al., 2008). Previous research also concerned mainly to parts of robot system, while an integration of all the components in a final specific model is not so often shown; the new virtual instruments made easier this kind of approach. Using these instruments and analyzing all individual parts within a unitary model, we expect to bring an increasing control over the system as whole. Further works is related to similar analysis for other parts of the kinematic chain for the analyzed robot; this allows integrating the parts within a system and observing and optimizing the structure, calculating the parameters (accuracy, stiffness, frequency, etc.) in order to increase the desired performance. Former work of the authors related to the first joint mechanism of robotic arm (Gramada et al., 2002) can be improved as well, considering the new research instruments available.

2. ANALYSIS AND RESULTS

2.1 The general model

First step of the analysis is to create the CAD model for the robot, considering the parts, joints and the structure and kinematic chain (Lenarcic & Roth, 2006); we have used Solid Works to create all the geometry of the robot.

In order to analyze the behavior of the kinematic chain parts of the robot such as mechanisms within the kinematic chain of the second joint of the articulated arm type robot and the way this influences over the general behavior of the robot, we have detailed a separate analysis in dedicated software for FEM analysis. The model have been exported in compatible file for Ansys specialized software which confer confident results, the geometry imported, updated and the structure meshed using triangular elements. The robotic structure was also modeled and analyzed in FEM in order to allow further optimization criteria. The calculus analysis of the stiffness (Nakasone et al., 2006) is based on the element stiffness equation (1) for the eth triangular finite and the element stiffness matrix [[k.sup.(e)]] (2), and forces (3) which are relevant for FEM further calculation:

[{P}.sup.(e)] = [[k.sup.(e)]][{[delta]}.sup.(e)] + [{[F.sub.[epsilon]0]}.sup.(e)] + [{[F.sub.F]}.sup.(e)] (1)

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (2)

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (3)

2.2 Robot structure model and structure analysis

For the FEM analysis of structure, we have considered the main input data as follows: distributed forces over Ox, Oy, Oz, end-effector load capacity of 50 kg., a temperature distribution in packaging area of 50[degrees]C. The structure static analysis comprises: the total deformation and directional displacement, principal stress and equivalent (von Mises) stress as well as frequency modes in range. The results are shown in the graphics below.

[FIGURE 1 OMITTED]

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2.3 Timing belt model and comparative results

The mesh model of the driven and drove pulleys includes 25,000 nodes of triangle elements while the belt 16,000 nodes of triangle elements considered as appropriate to obtain confident results.

The main results of the analysis of the second joint kinematic chain are summarized in the figures (3).

Running the simulation for the structure including the second joint effect, we have obtained the total deformation and directional displacements as shown in the figure (4).

The figure (5) shows a comparative analysis of Von Mises equivalent stress for the behavior of the structure and for the structure with the second joint mechanism included.

[FIGURE 3 OMITTED]

[FIGURE 4 OMITTED]

[FIGURE 5 OMITTED]

Comparative results of the maximum limits reached in terms of deformation are shown in the table (1) and (2).

The final step of optimization depends on what have to be improved which will determine the parameters to be analyzed. The analysis of parameters such as: deformation, stiffness or frequency must be considered in order to optimize the model.

3. CONCLUSION

An analysis of mechanical system for an articulated robot arm "RRR" type has been carried out. The analysis was done both previously and after considering the influence over the general accuracy and stiffness second joint over the global accuracy. After we have introduced the second joint, the parameters of deformation and stiffness of "RRR" structure has been improved. This because the damping impact of the joint is present. The first frequency is also increasing while maximum von Mises equivalent stress is decreasing.

All these results obtained contribute to evaluate the stiffness and the accuracy of positioning of the robotic structure considered. Although, we have analyzed only the effect of one rotational joint; for more accurate results, it is recommended to conduct further analysis which will include the other two rotational joints behavior and structure of the kinematic chain "RRR" type analysis. Further work will include also a "sensitivity analysis" considering several main criteria (parameters) in order to optimize the parameters in correspondence with the desired performances criteria such as: accuracy, stiffness, frequency behavior.

4. REFERENCES

Ghionea, I., Munteanu, G & Beznila, H. (2008). Von Mises Stress Evaluation for a Mechanical Part using the Catia Finite Element Method. Proceedings of the 19th International DAAAM Symposium, Katalinic, B. (Ed.), pp. 275-276, ISBN 978-3-901509-68-1, Vienna, October 2008 DAAAM International, Vienna

Gramada, Al., Ghionea, A., Ghiorghe, A. & Munteanu, G., (2002). Calculus aspects of the first rotation degree of industrial robot. Proceedings of the Annual Session of Scientific Papers IMT Oradea, pp. 111-116, ISSN 1583-0705, Oradea, May 2002, University of Oradea

Kanarachos, S.A. & Spentzas, C.N., (2004). Analysis of the flexible mechanisms using the conventional FEM. Proceedings of the Scientific Computing to Computational Engineering Athens, pp. 185-192, ISBN 960-530-069-9, National Technical University of Athens, September 2004, Patras University Press, Athens

Lenarcic J. & Roth, B. (2006). Advances in Robot Kinematics Mechanisms and Motion, Springer, ISBN 101-4020-4940-4 Dordrecht, The Netherlands

Nakasone, Y., Yoshimoto S. & Stolarski, T. A. (2006). Engineering Analysis with ANSYS Software, Elsevier Butterworth-Heinemann, ISBN 0-7506-6875-X, Oxford

Stanciu, M.; Nicolescu, A. & Minciu, C. (1999). Specific elements regarding elastic behavior of mechanical parts used for joint engineering of industrial robots: a. Static behavior analysis for contacts areas. b. Static behavior analysis of thin section bearings. Proceedings of the 10th International conference Tehnomus, pp., ISBN 973-940827-3, Suceava, May 1999, "Stefan cel Mare" University, Suceava

<TABLE INSERT>

Tab. 1. Frequency modes with and without "R" joint behavior

Frequency Modes 1st 2nd 3rd
in Range (Hz)

Structure only 51.57 58.95 153.24
Belt transmission 400.91 465.12 680.58
Structure with second joint 51.586 59.188 161.35

Frequency Modes 4th 5th
in Range (Hz)

Structure only 187.65 --
Belt transmission 783.57 933.81
Structure with second joint 200.12 266.24

Tab. 2. Analysis without/with rotational joint consideration

Parameter Total X axis Y axis Z axis
 deformation deformation deformation deformation

Before 0.374 0.110 0.265 0.054
After 0.134 0.044 0.015 0.004