Keywords: Ankle; Bionic; Auxiliary Rehabilitation Device; Simulation Analysis.

Transcription

1 07 International Conference on Mechanical Engineering and Control utomation ICMEC 07 ISBN: Simulation nalysis of Bionic uxiliary Device for nkle Rehabilitation Based on DMS Liang-Wen WNG a, Ya-Lin MU b, Hong-Peng LI c, Fan-Nian MENG d, Kang-Kang SONG e and Wen-Liao DU f School of Electromechanical Science and Engineering, Henan Key Laboratory of Mechanical Equipment Intelligent Manufacturing, Zhengzhou University of Light Industry, Zhengzhou 45000, China a w_liangwen@sina.com, b @qq.com, c @qq.com, d mengfannian3@63.com, e songzongkang@sina.com, f dwenliao@zzuli.edu.cn Keywords: nkle; Bionic; uxiliary Rehabilitation Device; Simulation nalysis. bstract. kind of auxiliary device for ankle rehabilitation based on a ball pin vice is introduced in this paper first. he device has two degrees of freedom, while three-dimensional movement of the ankle can be achieved approximately. Motion simulation is preceded by using DMS for researching its dynamics and kinematics performance when the upper platform adopts three motion rules to control the movement. he modeling and simulation of the device are described in this paper. he analysis results can be used to optimize structure and determine its characteristic parameter. process of this research can be as a reference for mechanism analysis of more motion models. Introduction In the field of rehabilitation medicine engineering, the research on ankle joint rehabilitation is one of the important research topic. Many scholars studied various ankle rehabilitation mechanisms. ypically, the University of New Jersey developed a parallel ankle rehabilitation robot based on the mechanism of Stewart, which has six degrees of freedom DOF []. Bian Hui[] proposed a -RRR/UPRR ankle rehabilitation robot; Matteo Malosio[3] Studied 3 DOF ankle and foot nerve rehabilitation facility; Z.M. Bia[4] developed a rehabilitation robot adopting 3 DOF spherical parallel mechanism, using three linear actuator, which reached a higher research level. In order to reduce the cost of manufacturing and use of the device, based on the researches for existing ankle rehabilitation mechanisms, authors developed a kind of auxiliary device for ankle rehabilitation based on a ball pin vice[5], and the device has two DOF, while three-dimensional movement of the ankle can be achieved approximately, namely dorsiflexion /plantar flexion movement, varus/valgus movement and the compound movement. Motion platform adopts different motion law will significantly change device movement characteristics[6].in order to study the influence of different motion laws on the performance of the device, this paper discusses emulation of the bionic auxiliary device for ankle rehabilitation based on DMS. he Structural Description of the Device he ankle join involves dorsiflexion/plantar flexion, varus/valgus and adduction/abduction. Dorsiflexion/plantar flexion and varus/valgus are main motions, which determine whether patients recover or not. In this paper, we study the bionic auxiliary apparatus for ankle rehabilitation. he core of device is the clever combination of the sphere-pin pair. he device includes the upper platform, center sphere-pin, lower platform, drive of dorsiflexion/plantar flexion, drive of varus/valgus and control systems. Motion for dorsiflexion/plantar flexion and varus/valgus are respectively driven by the servo motor, ball screw nut pair, spring, etc. he model is shown in Fig.. 376

2 In order to realize the three kinds of motion, three fulcrums of the rehabilitation device on each platform are arranged at right angles, and the mechanism diagram is shown in Fig.. When the rehabilitation motion of dorsiflexion/plantar flexion of the ankle is needed to be realized, the motor I works. he motor I rotates a screw 4 to drive a slide block 6.he slide block 6 presses the spring 7. Lower platform is used as a support. By using spring, the upper platform 8 is driven to deflect a definite angle along the direction of dorsiflexion/plantar flexion. he upper platform 8 can implement reciprocating movement. When foot joint is buckled on the upper platform 8, the dorsiflexion/plantar flexion motion of the foot is realized. flexible movable frame; upper platform; 3a dorsiflexion/plantar flexion driven mechanism; 3b introversion/extroversion driven mechanism; Figure. he Model of the Device. a b lower platform; motor; 3 u-shaped connecting piece;4 screw; 5 moving box; 6 slider;7spring;8 upper platform;9 ball pin structure a State of rotating α circling around X 0 axes for the device b branched chain of driving Figure. Schematic Diagram of Mechanism. 377

3 When motion range of the dorsiflexion/plantar flexion is smaller, only motor I works. While, when the motion range I is larger, motor II is also started to work. Similarly, when rehabilitation motion of introversion/extroversion for the ankle is needed to be realized, the corresponding motor works. When the complex rehabilitation exercise is needed, two motors work at the same time through the control system. Motion Model of the Device ssuming that the motor driving dorsiflexion /plantar flexion motion is motor I and the motor driving varus/valgus motion is motor II, there are five kinds of situations in the process of motion: motor I rotates, motor II does not rotate; motor II rotates, motor I does not rotate; 3 motor I rotates first, motor II follows to rotate; 4 motor II rotates first, motor I follows to rotate; 5 motor I and motor II rotate at the same time. Each case can be divided into three patterns: the transition mode namely, the motor moves and springs are pressed, while the upper platform cannot be driven; rigid-soft combination drive mode springs are pressed by the motion of motor, and the upper platform is driven by the spring. 3 rigid drive mode springs are pressed at solid position and the upper platform is driven by these springs. s shown in Fig., B, B and B 3 are initial positions, and B, B and B 3 are positions after the upper platform moves. he rotation center O of center ball pin is used as origin to establish the fixed coordinate system X 0 Y 0 Z 0, the coordinate system fixes on the lower platform. t the same time, the rotation center O is taken as an origin to establish the moving coordinate system X Y Z, which is fixed on the upper platform. Because the upper platform is a symmetrical structure, the centroid point of the upper platform is regarded as point P approximately. he point P is the center point of the line. he two coordinate systems are overlapped under the initial state. General Harmonic rapezoid Motion Law Figure 3 shows the general harmonic trapezoid motion law of motion curve, which combines the uniform motion curves, the acceleration curve and harmonic curve together, and makes full use of their advantages. By selecting the different i values, we can obtain a variety of movement rules with high performance which can be widely used in engineering practice. Here, we use three kinds of motion rules to control the motion of the upper platform, and analyze the related motion. Figure 3. General Harmonic rapezoid Motion Law. he curve is composed of 7 sections, and its acceleration expression is shown below: 378

4 = cos sin 0 cos 0 sin π π π π here are three kinds of commonly motion law curve : Modified Constant Velocity Motion Law he constant speed motion law is discontinuous on both ends. Harmonic transition curve is used at both ends, which can be used for medium and low speed and heavy load. Fig. 4 shows the this kind of motion curve. Figure 4. Modified Constant Velocity Motion Law. Modified rapezoid Motion Law he discontinuous segment of the constant acceleration motion law is transited with harmonic function transition, which can be used for medium and high speed occasions. Fig. 5 shows the this kind of motion curve. Modified Sine Motion Law he curve is consisted of three segments of harmonic curve, the both ends of the cosine curve is transited whit the sine curve. his kind of motion law not only maintains the small feature advantages of cosine curve V m, m, but also overcomes the shortcomings of the acceleration discontinuity at both ends of the two ends. he curve of comprehensive performance is good. Fig. 6 shows the this kind of motion curve. Figure 5. Modified rapezoid Motion law. Figure 6. Modified Sine Motion Law. Motion Simulation Based on DMS Structural parameters of the device are shown as follows: a=50mm, 379

5 b=50mml =704.mml 3 =.7mm, l 4 =69.4mm; he load on the upper platform:.kg; the rotational inertia circling around the X axis: J X =4375kgmm ; elasticity coefficient of the upper springs in the spring frame: K=5.55N/mm; elasticity coefficient of the following springs in the spring frame: K=7.4059N/mm; the quality of the upper platform structure: m=6.537kg, the mass of the moving box: m=.69kg. First, the mechanism model is established by using Solidworks, and saved into.x_t format. he model is imported into DMS, as shown in Fig.7. Figure 7. Simulation Model. In DMS, from the lower platform to the upper platform, the constraints are increased. he spherical and the inplane joint primitive is used to replace ball pin vice, the rotation direction is selected as the X axis and Y axis; the combination of screw pair, cylindrical vice and prismatic pair is used to replace lead screw nut pair, other parts without relative motion are connected by fixed pair. Rotation pair is added around the Z axis to simulate the motor rotation, which acts as the input of the mechanism. Using DMS, after motor is given a input function to simulate the mechanism, movement simulation analysis of the upper platform can be realized. he simulation in the State of Springs Being Not at Solid Position In this study, we only discusses that motor I rotates when the upper platform has a rated load and the spring is not pressed at solid position. he upper platform rotates around the Y axis due to the motor Is motion. he platform position can be expressed with the Euler angle β of the Y axis. he position function of the upper platform is modified constant velocity motion, modified trapezoid motion and Modified sine motion. he time of upward and downward movement of the upper platform is 5seconds, the angle is 30 degrees. First of all, the relationship curve between the motion angle ϕ and time t of motor I is plotted by the Matlab software. hen, the curve fitting functions is gotten by using the polyfit command. Finally, the fitting function is used as the input of motor I to simulate analysis in the DMS. For simulating, the elastic coefficient of each spring need to be set. he simulation time is set to 5 seconds, and the step size is set to 0.. he curves of the angular displacement, angular velocity and angular acceleration of the upper platform around the Y axis are output. he results are shown as Figs 8-3. he Upper Platform Moves Upward. he upper platform is driven by the modified constant velocity function, the output as shown in Fig

6 Figure 8. he ngle Displacement, ngular Velocity and ngular cceleration of Upper Platform around Y xis. he upper platform is driven by the modified trapezoidal function, the output as shown in Fig. 9. Figure 9. he ngle Displacement, ngular Velocity and ngular cceleration of Upper Platform around Y xis. he upper platform is driven by the modified sine function, the output as shown in Fig. 0. Figure 0. he ngle Displacement, ngular Velocity and ngular cceleration of Upper Platform around Y xis. 38

7 he Upper Platform Moves Down.he upper platform is driven by modified constant velocity function, the output as shown in Fig.. Figure. he ngle Displacement, ngular Velocity nd ngular cceleration Of Upper Platform around Y xis. he upper platform is driven by modified trapezoidal function, the output as shown in Fig. Figure. he ngle Displacement, ngular Velocity and ngular cceleration of Upper Platform around Y xis. he upper platform is driven by modified sine function, the output as shown in Fig. 3. Figure 3. he ngle Displacement, ngular Velocity and ngular cceleration of Upper Platform around Y xis. 38

8 Driving orque of Motor Shaft In order to study the driving torque of the motor, the rotation pair is added around the Z axis in the motor. he upper platform is loaded with. kg, which adopts the uniform load. When using different functions to drive, the moving platform moves up to the maximum position and moves down to the minimum position from the balance position,the drive torque of the motor shaft can be gotten. Drive torque curves are shown in Figs 4-5. MOION: Modified constant velocity function drive, MOION:Modified sine function drive, MOION3:Modified trapezoidal function drive. Figure 4. orque for Upper Platform Upward Movement. MOION5: Modified constant velocity function drive, MOION6:Modified sine function drive, MOION7:Modified trapezoidal function drive Figure 5. orque for Upper Platform Downward Movement. Compared analysis on drive torques, when the upper platform moves upward and is driven by modified trapezoidal function, the torque of the motor is fluctuating at the middle and end. t this point, using modified sine function drive is better than using the other two kinds of driving way. When upper platform moves down and is driven by the modified constant velocity function, the torque of the motor is fluctuating at the end. Modified sine function drive mode is better than the other two kinds of driving mode. 383

9 Conclusion In this paper, simulation analysis of the device is completed. he angular displacement, angular velocity and angular acceleration of the upper platform are obtained. he driving torque of the motor spindle is obtained for upper platform motion with different motion law to drive. he analysis result can be used to optimize the structure of the device. cknowledgements his work is supported by support plan of echnology Innovation eam of Henan Colleges and Universities, Key echnology Research Project of Henan Province and Doctoral Research Funded Projects of Zhengzhou University of Light Industry 06BSJJ009. References [] Girone M, Burdea G M, Bouzit V, et al. Stewart platform-based system for ankle telerahabilitation[j]. utonomous Robots, 00, 0: 03-. [] Bianhui, Liu Yanhui, Liang Zhicheng, et al. mechanism and kinematics of ankle rehabilitation robot -RRR/UPRR in parallel[j]. Robot, vol. 300, no., pp. 6-. [3] Matteo M, Simone P N, Nicola P, et al. Spherical Parallel hree Degrees-of-Freedom Robot for nkle-foot Neuro-Rehabilitation[C]//34th nnual International Conference of the IEEE EMBS. merica: San Diego, 0: [4] Bia Z M. Design of a spherical parallel kinematic machine for ankle rehabilitation[j]. dvanced Robotics, 03, 7: -3. [5] Wang L W, Mu X Q, Wang X J, et al. Design research of bionic auxiliary device for ankle rehabilitation based on the ball pin vice[c]//proceeding of the th World Congress on Intelligent Control and utomation. China: Shenyang, 04: [6] Wang Liang-wen, Li Hong-peng, Wang Xin-jie, et al. Simulation nalysis of Bionic uxiliary Device for nkle Rehabilitation based on Recurdyn [C].Proceedings of the International Conference on Mechatronics and utomation Engineering ICME06, China: Xiamen, 06: