Robotic arm modelling and analysis.

Toth-Tascau, Mirela ; Menyhardt, Karoly ; Stoia, Dan Ioan 等

1. INTRODUCTION

The upper limb prosthetics represents an interesting research field focused on the modelling, design, control and manufacturing of multifunctional upper limb prostheses. As assistive device, the robotic system can be used during the rehabilitation process for maximizing the manipulation and mobility functions.

The research developed in this field ranges from kinematic studies and dynamic control of grasping and limb mobility to advanced manufacturing technologies.

The general objective of the developed research was to model, design, analyse and manufacture upper limb prosthesis. The study was performed in the framework of a Romanian CNCSIS project Autonomous prehension system to support handicapped human beings or access into dangerous areas. The main studies were (CNCSIS Final Report, 2007):

* kinematic analysis of the upper limb having 12 degrees of freedom, based on Denavit-Hartenberg convention;

* modelling of the upper limb workspace;

* geometric modelling of a robotic arm and its workspace;

* kinematic and dynamic analysis of the robotic arm;

* design an upper limb prosthesis;

* experimental analysis of the manufactured prosthesis.

The presented paper is focused on some aspects of the geometric modelling of a robotic arm, modelling of the robotic arm workspace and kinematic analysis of the robotic arm.

2. MODELLING OF THE ROBOTIC ARM AND ITS WORKSPACE

2.1 Modelling of the robotic arm

Taking into account the daily activities of a human upper limb, robotic arms having different degrees of freedom have been design (Cheze et al., 1996), (Troncossi et al., 2005). The model was design based on anthropometric data selected from literature (Robertson et al., 2004). This simplified model of the robotic arm is able to execute complex movements, performing the common tasks of the human upper limb.

The model of the robotic arm is presented in figure 1. The robotic arm has four joints:

* joint A executing the flexion-extension movement of the end effector--wrist joint;

* joint B executing the pronation-supination movement of the forearm--wrist joint;

* joint C executing the flexion-extension movement of the arm--elbow joint;

* joint D executing a rotation in a plane oriented at 45o to the sagital plane--shoulder joint.

The joints are activated by three actuators with reductions which allow independent rotations of the joints. The shoulder joint is considered to be not activated. Its motion is performed under its own weight.

2.2 Modelling of the robotic arm workspace

In order to evaluate the movement abilities of the end effector, the workspace model has been simulated (Dragulescu, 2005). There are many computer programs that allow this modelling. In the presented study, the workspace was modelled using the Matlab environment. There are studied many cases taking into account different combinations of joint rotations. In figure 2 is presented the workspace obtained when all the joints are active.

The volume of the robotic arm workspace varies in the interval of 97 dm3 and 206 dm3 depending on the movement complexity and the combination of the activated joints. This volume covers the common movements of the human upper limb for daily activities.

3. KINEMATIC ANALYSIS

The kinematic analysis of the robotic arm can be performed using the well known methods from Robotics, different Engineering Software such as DMU Kinematics Work Bench, Pro/MECHANICA, etc. or simulation packages of CAD environments.

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SolidWorks Motion simulation package was used to study the kinematic behavior of the elaborated virtual model of the robotic arm. The kinematic analysis was performed taking into account the following conditions:

* shoulder joint is not activated by an actuator;

* elbow joint executes a flexion-extension motion in the interval of [0[degrees], 150[degrees]];

* wrist joint executes flexion-extension motion in the interval of [-60[degrees], +60[degrees]] and pronation-supination motion in the interval of [-90[degrees], +90[degrees]].

The start configuration was considered to correspond to 0[degrees] for the shoulder, 0[degrees] for the elbow and 60[degrees] extension--90[degrees] supination for the wrist. The time interval for the test was of 10 seconds and the considered frequency was 0.1 Hz.

The reference frames used for the kinematic analysis are presented in figure 3. The reference frame attached to the end effector has the origin O' in the mass centre of the hand. The motion of this point was studied with respect to the reference frame attached to the shoulder.

The kinematic analysis was performed taking into account the motion in each joint separately and different combinations of joint motions in sagital plane (xOz). The following graphics (figures 4 and 5) represent displacements, velocities and accelerations along Ox and Oz axes obtained in the case when the elbow joint executes flexion-extension motion and there is no motion in other joints.

The shoulder was considered as a passive joint, thus the x-axis graphs are unstable due to the gravity and inertia acting on the robotic arm. This aspect is most visible on the acceleration graph where the curve presents many variations during the considered time interval.

The z-axis curves are smoother both for the ascending and descending parts, because gravity tends to compensate for the inertia and thus helps the actuating system to run with less noise.

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4. CONCLUSION

The workspace modelling and kinematic analysis are useful to evaluate the prosthesis mobility. The designed model of the robotic arm is able to execute complex movements and perform common tasks of the human upper limb.

The considered robotic arm represents a simplified model of the human upper limb being composed of rigid bodies. The virtual model of the robotic arm was created using SolidWorks environment and Motion Simulation was then used to analyze the model motion. In order to obtain more realistic information, more complex mechanical structure must be designed and a full range of physical phenomena, including, mechanical dimensions, weight, mass distribution, moments of inertia, actuators, torque, friction in joints, dynamic and static loads, etc will be considered.

The purpose of this study was to support future researches by easing the design phase for artificial upper limb. The next step will consist in realising of a control system that can compensate the different forces acting on the prosthesis, in order to obtain smoother curves for kinematical parameters. The goal of the dynamic analysis will be to determine the kinetic moment and the power consumption for each considered joint. Finally, the analyzed robotic arm model will be used to design lower cost upper limb prosthesis.

5. REFERENCES

Cheze, L.; Gutierez, C.; San Marcelino, R. & Dimnet, J. (1996). Biomechanics of the upper limb using robotic techniques, Human Movement Science, Vol. 15, No. 3, June 1996, pp. 477-496, Elsevier, ISSN 0167-9457

Dragulescu, D. (2005). Modelarea in Biomecanica (Modelling in Biomechanics), Editura Didactica si Pedagogica, R.A., ISBN 973-30-1725-6, Bucuresti

Robertson, D.G.E.; Caldwell, G.E.; Hamill, J.; Kamen, G. & Whittlesey, S.N. (2004). Research methods in biomechanics, Human Kinetics Publishers, ISBN 073603966X, Champaign

Troncossi, M.; Parenti-Castelli, V. & Davalli, A. (2005). Design of upper limb prostheses: A new subject-oriented approach, Journal of Mechanics in Medicine and Biology, Vol. 5, No, 2, June 2005, pp. 383-390, ISSN 1793-6810

*** (2007). CNCSIS Final Report of Romanian project Autonomous prehension system to support handicapped human beings or access into dangerous areas.