The 3rd Joint International Conference on Multibody System Dynamics The 7th Asian Conference on Multibody Dynamics June 30-July 3, 2014, BEXCO, Busan, Korea
Towards the elaboration of 3D dynamic model for push/pull cable (PPC) actuation system Svetlana Grosu*, Chris Verheul#, Carlos Rodriguez-Guerrero*, Bram Vanderborght* and Dirk Lefeber* *
Department of Mechanical Engineering Vrije Universiteit Brussel Pleinlaan 2, 1050 Brussels, Belgium [sgrosu, carodrig, bram.vanderborght, dlefeber]@vub.ac.be
#
SayField International Broeksloot 10, 3474 HP Zegveld, The Nederlands
[email protected]
ABSTRACT A push/pull cables (PPC) can be used as an effective alternative to replace complex, heavy transmission mechanisms while providing flexible power actuation with a bi-directional (push and pull) mechanical force driving. Due to the structural advantages of the cables, the PPCs are especially appreciated in robotics. In regard to proposed here study, the authors main focus was to develop a complex multibody dynamics PPC model for the orthosis actuation system of a novel gait rehabilitation device. This study combines development and simulation results of a single push/pull cable element 3D model and, afterwards, cosimulated with test-stand mechanical setup of a novel gait rehabilitation robot. The dynamic behaviour and technical specifications of these two compound devices have been observed and investigated in virtual environment, providing a valuable input in knowledge regarding the dynamics for general push/pull force transmission systems.
1. INTRODUCTION Gait training, over ground or on a treadmill, has become an essential part of rehabilitation therapy in patients suffering from gait impairment caused by disorders such as stroke, spinal cord injury, and multiple sclerosis. A focus on the human in collaboration with a robot puts emphasis on the adaptability and task specificity of robotic assistance required to achieve "assistance-as-needed" [6]. At the same time, safety of interaction, preventing harm and discomfort engages mandatory position. Hence, in the development of novel rehabilitation prototypes engineers are faced with the challenge of combining suitable design concepts, high performance actuator technologies and dedicated control strategies in view of improved physical human-robot interaction. Improvement, that should lead to a better insight into the effectiveness of robot-assisted rehabilitation and ultimately, leads to qualitative therapies. Gait rehabilitation robots can be categorized according to their underlying kinematic concept into endeffector based and exoskeleton based robots [9]. End-effector based robots interact with the human body in a single point (through their end-effector), whereas exoskeleton based robots interact with the human body in different points across human joints. Most gait rehabilitation robots are exoskeleton based and prototype development in this type of devices is often supported and stimulated by advancements in related applications: rehabilitation and assistive exoskeletons, human performance augmenting exoskeletons and powered prosthetics, see Figure 1 There are several contributions in literature presenting an overview regarding existing lower limb rehabilitation robotic systems [3, 5, and 10] and discussing a specific design challenges along its development. Common actuators have important drawbacks for use in a rehabilitation exoskeleton. Either the actuators are heavy, complex or poor torque providers. Tension cables are used widely in mechanical systems for transmitting forces or displacements between driver and driven parts in diverse range of applications where the usage of classic linkages becomes unpractical.
Figure 1. Gait Rehabilitation Robots: end-effector based ( e.g. Gait Trainer GTI) and exoskeleton based (e.g. CORBYS. Related applications supporting the development of exoskeleton based gait rehabilitation robots: human performnce augmenting exoskeletons (e.g. HAL), assistive exoskeletons (e.g. ReWalk), powered prosthetics (e.g. C-leg)) The cable efficiency depends on occurrence such as friction and stretching, the configuration of the cable and material. Because transmission paths of the cables are often convoluted, modelling the dynamic behaviour is challenging. Hence, cable structures have complex static and dynamic behaviours due to their non-linear geometric properties. Push/pull cables (PPC) - the type of tension cables, effectively can replace complex and heavy transmission mechanisms and accomplish the function to transmit mechanical force in push and pull directions. The PPC represent a type of flexible cable used to transmit mechanical force or energy by the movement of an inner cable, usually made of stainless steel, relative to hollow outer cable housing. The movement of the inner cable is used to transmit a pulling or pushing force. A flexible Bowden cable transmission was implemented in gait rehabilitation robot for treadmill training LOPES [19, 20], which combines a lightweight joint, simple structure while providing an adequate torque source quality. The main reason in using the PPC actuator in exoskeleton robotic device is because of possibility to detach the actual motor from the robot orthosis leg, so that exoskeleton can move unhindered. Because the topic of this paper is regarding PPC evaluation of dynamic behavior with all inherent nonlinearities, a short review of literature describing cables modeling in virtual environment is presented below. Nowadays, computational methods, modelling and simulations gained a considerable recognition in various phases along a project development, as an efficient and relative inexpensive evaluation method. Several contributions proposed in literature have dealt with the problem of modelling and predicting positive cable tensions, in conditions that cable forces are maintained tensile [13]. In other words, cables can only pull the end-effectors, but not push on it. The estimation of cable tensions and configurations has been for long an area of considerable research effort. Static cable problems have found application in the design of buoy [2] and mooring systems [18] where the maximum cable tension is an important concern. The continuous and discrete modelling approach for static behaviour of cables, are elaborated in a number of papers [12, 15, 4]. Also, there are the papers with non-linear static and dynamic analysis of cables [16, 11], where one of the following modelling approaches is used: (1) the finite element method, based on polynomial interpolation functions or (2) the analytical approach. The second approach suggests the usage of elastic catenary exact analytical expressions, in order to describe the realistic behaviour of cables. But, all works mentioned so far were limited to the cable investigation in tension, stretched form. Linear models which describe the essential linear behaviour of the tensile cables were proposed in contributions [20, 17, and 18]. A 3D dynamic modelling approach of the cables in mechanical setup of powered prosthesis was proposed in recent publications, where general dynamic parameters were evaluated [7, 8]. In addition, an analytical model for a push/pull cable was proposed in [1], where the dynamic model uses discrete elements and predict backlash, cable slacking and other nonlinear behaviour.
To our knowledge, there is a lack of published studies on 3D modelling and simulation of PPC parameters such as: the dynamic behaviour of inner cable relative to the outer, estimation of friction between the cable and the conduit, effect of external forces applied to the inner cable. Therefore, in present paper the authors will investigate particularities of the PPC's and will present obtained results based on simulations in virtual environment.
2. PPC ACTUATION SYSTEM FOR ORTHOSES This section provides a detailed description of general PPC technical specifications as an individual mechanical sub-system. Afterwards, the design and implementation of PPC actuation system is presented in framework of a novel gait rehabilitation device - CORBYS and simplified version of this, a test-stand setup. 2.1.
PPC technical specifications and terminology
Push-pull control assemblies are designed to provide smooth, positive and precise transmission of mechanical motion for medium to heavy-duty push-pull applications. The general structure of PPC consists of an inner member, made from a wire rope and armored with a polished flat band wrap covered with an inner tube. The inner tube is armored with a tough but flexible steel tube built up out of steel wires armored with a flat steel covering band. The extern layer is represented by an extruded plastic mantle of great strength and durability, see Figure 2. The inner member can easy slide in low friction lifetime lubricant. Also, the end borders of the cable are featured with stainless materials and effective seals, which have a role to assure protection against foreign matter and corrosion. The PPC are confectioned from thermoplastic materials in form of knobs or as covering of assemblies. These materials can include Polypropylene, Acetal Resin and Nylon.
Figure 2. General structure of push/pull cable Due to the wide range of applications, various types of PPC are used, with features optimized for the certain domain of activity and which can meet specific parameters of the system. The parameters such as temperature range, frequency, loads limits, flexibility and bend radii compose the requirements that PPC should handle with high efficiency. The efficiency of a PPC is represented by relationship between required input force and the given output load. Also, it is high dependent on the number of bends along cable lay. Efficiency factor ratings are for comparative purposes and may vary due to length, rate of travel, direction of travel, bend radius and temperature. In this sense cable features as: structural modifications, cable size, end connectors type, travel length and cable length should be adapted conform applicability needs. The selection of the proper push-pull control for any application is generally a function of the input force required. This force, in turn, is dependent on the output load and the efficiency of the assembly. Friction between the inner core member and the primary tube will have the greatest impact on the assembly efficiency. The friction factor will be dependent upon the total degrees of bend in the system. 2.2.
PPC in framework of CORBYS project
CORBYS - Cognitive Control Framework for Robotic Systems is an International Project funded by the European Commission under the 7th Framework Program [21]. CORBYS aims to design a cognitive control architecture that allows inclusion of high-level cognitive control modules, a semantically-driven self-awareness module and cognitive framework for anticipation of human behaviour. This objective concerns the development of a perception system for assessing the physical and mental state of the environment including humans. Two directions of information exchange will be considered:
- human to robot - cognitive information related to the human intention and of the human cognitive monitoring during the execution of the task (e.g. degree of attention and relaxation); - robot to human - cognitive information related to the robot perception of the human execution and how this information is perceived by the human (feedback errors).
a) b) Figure 3. a) CAD of CORBYS gait rehabilitation platform; b) CORBYS PPC actuation system Structurally, CORBYS includes a combination of a mobile platform and powered orthoses actuated at the knee, ankle and hip joints, see Figure 3.a. The actuation system, see Figure 3.b, is based on using PPCs to transfer the rotational movement of the motors to specifically designed joints on the orthoses. Therefore, the rotary movement of the actuator has to be transformed to a linear movement in order to actuate PPC. This transmission is provided using a mechanical lever construction. The applicable force obviously depends on the lever length and position. Forces can be used only if directed to the PPC, all other directions are lost power. The transmitted force changes with the lever position (angle). This means the wider the operation range of the actuator, the smaller is the applicable force in PPC direction. The force applied by the actuator therefore is reduced by the lever and the friction in the PPC. The efficiency of the PPC is essential for the function of the powered orthosis. The maximum deflection of the PPC has been restricted to 8° in each direction. The actuators for the active joints are placed in a proximal way back on the mobile platform while the PPC is a flexible link to the joints. The static (non-moving) part of the PPC is to be mounted to the demonstrator base profile frame. The distance from the smart actuators centre to the static attachment of the PPC depends on the necessary stroke of the PPC. This stroke is given by the kinematic design of the orthotic joints. Each joint (hip, knee, and ankle) has a different kinematic design and therefore a different stroke parameter. 2.3.
PPC in test-stand setup
Because the developing of CORBYS prototype is still ongoing, in the initial phase of testing and evaluation process have been designed and built a test-stand setup by project partners SHUNK and OB. This test-stand was designed in order to test the function of the smart actuator driving the orthotic joint using the PPC in between, see Figure 4.a.
Figure 4. a) Test-stand design; b) Force transmission from actuator to PPC
The test-stand setup includes the similar actuation system as in CORBYS project. Structurally, the teststand setup is including a frame part, supporting three motor elements and a leg's segment. The leg is composed of three revolute joints, at the ankle level, at the knee and at the hip. Three push/pull cable elements were implemented by connecting to the actuator and each joint of the leg. In the Figure 4.b is illustrated the principle of force transmission from the motor to PPC element, where
A : results from the desired stroke on the orthotic joint as well as the PPC size
r: lever length on the actuator
l: length of the mechanical connection
The desired stroke resulting from the geometry of the specific orthotic joint was specified during the design progress. The general technical properties of PPCs, selected for a specific application needs and mechanical setup are illustrated in Table 1. Table 1. PPC technical specifications Leg joint Hip Knee Ankle
Outer cable size 17.6 mm 13.3 mm 8.8 mm
Travel code 152 mm 102 mm 102 mm
Cable length 130 cm 130 cm 150 cm
Min bend radius 153 mm 76 mm 51 mm
Stroke (mm) 152 mm 102 mm 102 mm
Further, the test-stand setup will be referred in this research contribution, where a 3D model was built and simulated in MSC Adams multibody dynamics software environment [22].
3. MODELLING IMPLEMENTATION This section addressing modelling and simulation methods of push/pull cables dynamic behaviour, first, as a single independent element and, afterwards, implemented in a test-stand setup of a novel gait rehabilitation prototype. 3.1.
Single push/pull cable element
The PPC is represented in MSC Adams by a series of rigid cylinder PARTs distributed along the desired curvature of the cable centreline, see Figure 5.a. The curvature is described using SPLINE object between two end points of cylinders. By applying a SPLINE fitting method the equidistant points were created on the SPLINE. The discrete outer cable is built using a series of Hooke joints on the SPLINE points and cylindrical joints halfway. Geometrical, the outer cable is represented by a segments composed of rigid cylinder PARTs. An inner cable is represented by spring-damper geometry and has the property to stretch along the axis between each set of Hooke joints. When summating the complete deformation of all point point forces and then generating one common extension-compression force we can describe the complete inner cable behaviour. The forces are using the overall axial load of the cable and are exerted at the locations of the Hooke joints. This ensures that, while bending the cable, the length of the inner and outer cable remains identical.
Figure 5. a) 3D PPC segment representation; b) Radial and actuation forces represented during simulation of PPC single element
The model also takes into account all effects related to the axial and bending stiffness of the outer cable and the axial stiffness of the inner cable. The axial stiffness is the cable resistance to being compressed or elongated by an axial force. Resistance to bending is characterized by bending stiffness. And it has to do with the size of the cross section, but also with the shape. The axial friction force is represented by sum of radial forces between inner and outer parts of the cable, implemented in a Coulomb friction law, Figure 5.b. Using ToolKit Creator toolbox [23] the visual and dynamic properties of the PPCs can be facile adjusted conform specific application, see Figure 6.
Figure 6. GUI interface for dynamic properties of the PPCs In 3D PPC model we assume applying friction force at begin and the end of the inner and outer parts. The stick slip effect of the axial motion has not been included as it was only considered a velocity law for the generation of the slip and therefore friction coefficient by changing the velocity value where a full slip is occurred. The performed simulation results can be visualised in section 4 of present contribution. 3.2.
Push/pull cable actuation test-stand setup
In order to evaluate functionality of PPC model a 3D model of test-bed mechanical setup was implemented in MSC Adams. The test-bed model was imported from CAD software and, similar to the real setup, is composed of frame part, supporting three motor elements and one leg. All materials and dimension properties were also adapted conform the real system specifications.
Figure 7. 3D model of test-stand setup including PPC actuation system
The leg is composed of three actuated joints: at the ankle level, at the knee and at the hip. Three push/pull cable elements were implemented by connecting to the frame part through prismatic joints and each joint of the leg using fixed joint constraints, see Figure 7. An axial push and pull force is applied to the inner end part of the cable placed on a frame part. Physical parameters of the PPC were adjusted close to the real ones. Thus, stiffness and damping values were determined experimentally by performing a number of simulations; also friction values obtained from experiments were implemented to the model. An actuation force was applied to the PPC on the knee level, while other two remain passive. The obtained results based on co-simulation of test-stand subsystem with push/pull cable actuation sub-system are presented and discussed in a following section.
4. RESULTS & DISCUSSION This section includes the obtained results on simulation experiments and provides an interpretation of graph representations.
(1)
(3)
(2)
(4) Figure 8. Dynamic parameters of single PPC model
In Figure 8 are illustrated dynamic parameters of the single PPC element based on simulations in virtual environment. In the first graph an actuation force of inner member has negative values because of inverse modeled sign of the applied force. Friction force between the inner and the outer parts of the PPC is represented in a second graph. The force magnitude is relative small; this fact suggests a conclusion that friction between inner and outer parts of PPC isn't the main parameter that should be taken in account in control implementation in case of this PPC type. At the beginning of simulation one can observe an increased value of friction force which can be explained as static friction force. The third graph represent the displacement of inner member relative to the outer part, this parameter can be specified during modeling process of the cable. And, finally, the last graph illustrates length of the inner cable and its physical elongation along simulation exercise. Any another measurements of PPC single element model can be performed in MSC Adams software function of specific test objectives.
Figure 9. Friction measurements for 3 PPCs during co-simulation with test-stand setup In Figure 9 are represented obtained results of friction force for 3 PPC cables co-simulated with test-stand device. Because just PPC at the knee level has been actuated, one can observe increased values of friction force relative to the other two. Comparing to the independent PPC element one can observe the same small friction force values of inner and outer cables.
5. CONCLUSIONS PPCs dynamic behaviour has been modelled and analysed independently and in co-simulation with testbed setup. The main conclusion from this study is that friction force between inner and outer part of PPC is relative small and will not influence significantly control implementation and dynamics of CORBYS device, and it was observed that actually stiffness of PPC can have an impact on behaviour of the PPC actuation system. Also, thanks to developed PPC models, where all design parameters can be adjusted conform the real specifications, the dynamics of the push/pull cable actuation system can be predicted. For following work the authors propose to perform experiments with real test-stand device in order to validate obtained results, based on simulations.
ACKNOWLEDGMENT This research was supported by the European Commission as part of the CORBYS (Cognitive Control Framework for Robotic Systems) project under contract FP7 ICT-270219. Also, we would like to acknowledge OB and SHUNK partners for development of test-bed and CORBYS robot mechanical design.
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