Gabriel Szymkiewicz, Olga Szymanowska, Donat Lewandowski, Jan Awrejcewicz

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1 Hydraulic unit of rotation into linear motion conversion design, model, construction and testing Gabriel Szymkiewicz, Olga Szymanowska, Donat Lewandowski, Jan Awrejcewicz Abstract: An attempt to develop a unit which can be employed to solve problems connected with the manoeuvrability of prosthetic hands, surgical equipment and other systems requiring high stiffness and precision combined with good recurrence of movements in linear motion is made. The main goal is to reduce the cost of the device and to make its design less complicated comparing to already existing ideas presented by other researchers. Two conceptions of a unit used to convert rotary motion into linear one are presented, including variants employing a fixed step motor or a rolling guide. Sets of physical, mathematical and simulation models of the systems are developed and presented. Working prototypes based on the conceptions are manufactured and described. The research is supplemented with results of tests of the prototypes regarding their precision and stiffness. 1. Introduction Prosthetic technology aims to provide the patient who lost his hand with a replacement allowing to restore manoeuvrability as close as possible to that of the lost hand. Therefore, the goal of modern hand prostheses is to physically resemble a human palm. The attempts to mimic a natural palm have been made for some time, with the examples of the Utah/MIT hand, the Salisbury hand or the Barrett hand [6] which while properly imitating the motion of a human hand are also suitable for robotic manipulators. A good example of approach combining both manoeuvrability and ergonomics is the Fluidhand [7], a hydraulic hand, employing micropumps and flexible actuators. The greatest disadvantage of this design is high overall cost and complicated design of the prosthesis. Another interesting design is the Khefa hand [8]. The prosthesis uses segmented fingers connected by means of rubber hinges to shape memory alloy (SMA) cables providing the necessary motion. Main disadvantages of the design are the heat production and placement of the electrical system inside the hand. The goal of this work is to provide a simpler and cheaper solution for driving prostheses of upper limbs as well as for surgical equipment and for all applications requiring high stiffness and precision combined with good recurrence of movements in linear motion. The idea of the project is to employ a step engine connected to the driving actuator to create the flow of hydraulic oil through the tube and thus to induce the motion of the executive actuator. 493

2 2. Overall idea Figure 1. Conceptual drawings of the unit, a) variant with fixed step motor, b) variant with a rolling guide. 1 step engine, 2 driving actuator, 3 compensatory container, 4 hydraulic tube, 5 executive actuator, 6 rolling guide, φ rotation of the step engines shaft, x, y linear motions of the actuators. Figure 1 depicts two considered conceptions of the unit. In the first variant the piston of the driving actuator has an internal thread while the shaft of the step engine is threaded externally. The rotation of the shaft causes the motion of the actuator s piston and the combination of these two elements forms a pump creating the flow of the hydraulic oil into the executive actuator. The spring in the driving actuator ensures the withdrawal of the piston during backwards motion The principle of operation of the second unit conception is similar. The cylinder of the driving actuator is internally threaded. The shaft of the step engine screws into the cylinder during engine s rotation, creating the flow of the oil. In order to allow for free movement and reduce the drag, the step engine is placed on a rolling guide. This conception has been chosen for further development due to lesser complexity of the driving actuator. 3. Modelling In order to predict the behaviour of the unit, two sets of physical, mathematical and simulation models have been created. 494

3 Figure 2. The physical model of the unit. x, y linear motion of actuators, p1, p2 pressure of the hydraulic oil inside the driving actuator and the executive actuator, V10, V20 initial volumes of the actuators, E modulus of elasticity of the hydraulic oil, S2, m2 area and mass of the piston of the executive actuator, c2, α - viscous and Coulomb damping ratio between the piston and the cylinder of the executive actuator, k capacity of the hydraulic tube, k2 stiffness of the spring inside the actuator, F2 external force. Based on the physical model presented in Figure 2, three differential equations have been created ( ) where two of them concern the flow balance inside the system (the first one represents the output from the driving actuator, the second one representing input to the executive actuator) and the third equation describes the force balance in the executive actuator. These three equations form the mathematical model of the unit. (1.1) (1.2) (1.3) The model can be transformed into a dimensionless form ( ). (2.1) (2.2) where: (2.3) ; ; 495

4 ; ; ; ; ; ; ; ; ; The speed of the piston of the driving actuator is the control value. It is assumed that the motion resistances in this actuator are compensated by adequately powerful step engine. The aforementioned mathematical model is used to create a simulation model in Matlab Simulink environment with the simulation time τ = 1. Another values of parameters used in the simulation are as follows: = 0,01+0,005sin(1000t) [m/s]; S1 = S2 = [m]; V01 = V02 = [m3]; m2 = 0,03 [kg],; c2 = 117,3 [N s/m]; k2 = 195 [N/m]; k = 7, F2 = 10 [N]. The results of the simulation are presented in Figures 3 7. Figure 3. The positions of the pistons - of the drive actuator x ( ) and the executive actuator y ( ) at the beginning of the simulation. 496

5 Figure 4. The positions of the pistons - of the drive actuator x ( ) and the executive actuator y ( ) at the end of the simulation. As it can be observed on the above graph, at the end of the motion sequence, the difference between the positions of two actuators pistons equals to about 0.03 mm, which thereby gives positive predictions for the unit s precision. Figure 5. The velocities of the pistons - of the drive actuator ( ) and the executive actuator ( ) for the first ten milliseconds of the simulation. The application of the external force F 2 causes the velocity of the executive actuator to oscillate briefly, however the unit returns to the previous state within less than 5 milliseconds. 497

6 Figure 6. Velocities of the pistons - of the drive actuator ( ) and the executive actuator ( the first 10 milliseconds of the simulation. ) for The phase shift between velocities of both actuators pistons is 1 millisecond. Figure 7. The pressure of the hydraulic oil inside the drive actuator p 1 ( ) and in the executive actuator p 2 ( ). The application of the external force F 2 causes the pressure inside the unit to increase by 0.3 MPa. This behaviour allows the unit to stabilize the velocity of executive actuator s piston. 4. Working prototype. After choosing the conception and creating a simulation model, a working prototype of the unit has been designed and created. In order to test the principle of operation of the unit, it has been solely necessary to create the drive actuator and to connect it to a ready-made hydraulic executive actuator. 498

7 1. 2. Figure 8. Schematic diagram of the drive actuator. 1 threaded piston, 2 cylinder. Free space inside the cylinder of the actuator allows to test it in two configuration. The first one, shown in Figure 8, is identical to the chosen conception. The sealing of the unit is supposed to be provided by accurately tight thread on both the piston and the cylinder. In the second configuration, additional elements are added in order to provide better sealing. Figure 9. Schematic diagram of the drive actuator in second configuration. 1 threaded piston, 2 cylinder, 3 intermediate piston, 4 spring, 5 seal, 6 metal ball. The motion of the threaded piston directed into the cylinder pushes the intermediate piston equipped with a lip seal. The spring enforces the intermediate piston to withdraw the backwards motion. The metal ball reduces the friction between two pistons. Based on the above schematics, a prototype of the actuator has been manufactured. 499

8 Figure 10. Drive actuator connected to a step motor with a roller guide. Material chosen for the cylinder was bronze, due to low friction ratio regarding steel pistons. 2 Figure 11. Hydraulic unit test station. 1 drive actuator, 2 step motor with rolling guide, 3 executive actuator, 4 step motor driver, 5 displacement gauge, 6 control panel, 7 power source. First tests of the basic configuration (Figure 8) have showed that achieving necessary tightness of the threads is not possible with accessible technology. The result is an excessive leakage of the hydraulic oil. Thus, the tests have been performed on the second configuration of the actuator (Figure 9). 500

9 5. Unit precision test 2 Figure 12. Drive unit with scale disc (1) and displacement 1 gauge (2). In order to observe the rotation of the drive actuator, a scale wheel has been installed on the threaded piston. Observations of the movement of the executive actuator have been performed with the use of a displacement gauge applied to the actuator s piston. Considering the pitch on the threaded piston equal to 1 mm, one rotation corresponds to 1 mm of linear motion. Due to difficulty of observing the scale wheel with a naked eye, the test has been recorded with a camera and subsequently replayed frame by frame. During the tests, the difference between positions of two actuators has not exceeded 0.03 mm. 6. Stiffness test To test the stiffness of the unit, an external force has been applied to the piston of executive actuator, measured with the help of a dynamometer. The motion of the piston has been measured with the displacement gauge. The initial force was equal to 10 N and the piston has responded by means of moving by 0.01 mm. Then, the force has been increased up to 20 N and the piston again moved for 0.01 mm. The test allowed to calculate the stiffness of the whole unit (6.1). (6.1) 7. Conclusion The first tests of the described unit give good predictions regarding unit s precision and stiffness. With further development, the hydraulic unit of rotation into linear motion conversion can be a good solution for driving artificial limbs and surgical equipment, allowing to place the drive actuator 501

10 outside the patient s body and to use the hydraulic tubes to connect it to the executive actuator driving elements placed inside. Another possible application of the unit is in the industrial equipment requiring high level of precision regardless of applied loads. In further tests, it will be necessary to check the correctness of the units positioning after a series of set motions with different loads applied. In order to test the first configuration of the drive actuator, the unit must be recreated with much tighter thread, both on the cylinder and the piston. In order to minimize the leakage, the fissure between two threads should not exceed 5 μm. 8. References [1] Awrejcewicz, J. Mathematical Modeling of Systems, WNT, Warsaw, 2007, in Polish. [2] Bukowski, J. Fluid Mechanics, PWN, Warsaw, 1976, in Polish. [3] Kurmaz, L.W., Kurmaz, O.L. Design of Constraints and Machine Elements, Kielce University of Technology Press, Kielce, 2006, in Polish. [4] Stryczek, S. Hydrostatic Drive. Part 1: Elements, WNT, Warsaw, 2003, in Polish. [5] Stryczek, S. Hydrostatic Drive. Part 2: Systems, WNT Warsaw, 2003, in Polish. [6] Tai, E. Design of an anthropomorphic robotic hand for space operations. M.Sc. thesis, University of Maryland, USA, [7] Gaiser, I.N., Pylatiuk, C., Schulz, S., Kargov, A., Oberle, R., Werner, T. The Fluidhand III: a multifunctional prosthetic hand, JPO Journal of Prosthetics and Orthotics 21, 2 (2009), 1-6. [8] El-Sheikh, M. A., Taher, M. F., Metwalli, S. M. New optimum humanoid hand design for prosthetic applications, International Journal of Artificial Organs 35, 4 (2012), [9] Carrozza, M. C., Massa, B., Micera, S., Lazzarini, R., Zecca, M., Dario, P., The development of a novel prosthetic hand - ongoing research and preliminary results, IEEE/ASME Transactions on Mechatronics 7, 2 (2002), Jan Awrejcewicz, Professor: Department of Automation, Biomechanics and Mechatronics, Lodz University of Technology, Łódź, Poland Donat Lewandowski, Professor: Department of Automation, Biomechanics and Mechatronics, Lodz University of Technology, Łódź, Poland Gabriel Szymkiewicz, M.Sc. (Ph.D. student): Department of Automation, Biomechanics and Mechatronics, Lodz University of Technology, Łódź, Poland Olga Szymanowska, M.Sc.: Department of Automation, Biomechanics and Mechatronics, Lodz University of Technology, Łódź, Poland 502

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