A NEW ROBOT-BASED SETUP FOR EXPLORING THE STIFFNESS OF ANATOMICAL JOINT STRUCTURES. [Frey, Burgkart,

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1 A NEW ROBO-BASED SEUP FOR EXPLORING HE SIFFNESS OF ANAOMICAL JOIN SRUCURES Martin Frey 1, Rainer Burgkart 2, Feli Regenfelder 2, and Robert Riener 1 1 Institute of Automati Control Engineering, ehnishe Universität Münhen, Germany 2 Clini for Orthopedis and Sport Orthopedis, ehnishe Universität Münhen, Germany [Frey, Burgkart, Riener]@vr-om INRODUCION One method for analyzing the biomehanis of human joints is to apply fores and torques to the joint and detet the resulting displaement From this ontet between load and displaement the elasti aspets of the knee joint an be estimated Many groups work on olleting suh data and many different setups eist for performing suh measurements Several authors tried to measure elasti aspets of human knee joints in vivo A setup to measure the laity of the ollateral ligaments not at adavers but at patients is used in [Moore] Varus and valgus torques were applied to the knee joint and the displaement was measured he problem when applying torques or measure displaement in vivo is the moving soft tissue between fiation of the measurement apparatus and the bones of the leg Eat measurements an hardly be perfor Furthermore, no measurements of both the intat and injured knee joint at a single patient are possible hus, most groups use human adaver knee joints for aquiring biomehanial data Markolf presented lots of measured biomehanial data from human adaver knee joints [Markolf] He built up several setups for measuring the elasti harateristis for various degrees of freedom he displaement was measured with eternal fied potentiometers, the fores with strain gauges mounted to the handle and the fiation of the adaver bones Woo in Pittsburgh, USA [Fujie, Woo] presented the idea of using an industrial robot ombined with a universal fore torque sensor for performing biomehanial measurements he idea was realized with a 6 DOF industrial robot In the meantime other working groups piked up this idea Neme [Neme] at the Jozef Stefan Institute Ljubljana, Slovenia is using a Riko 16 robot for testing kinematis of synovial joints Hurshler [Hurshler] of the Hanover Medial Shool, Germany is using a KUKA 16 robot for simulating arm fores while testing the shoulder joint he setup presented in this artile is using the high preision industrial robot Stäubli RX9-B, whih is well known as Ortho Marquet s Caspar Novel is the ustom made highly dynami losed loop ontrol hard- and software of the robot his enables to do fast measurements, so a lot of tests an be perfor with a single adaver A speifi hybrid ontrol arhiteture has been implemented for testing knee joints with various load onstellations Figure 1: Coordinate systems COORDINAE SYSEMS he oordinate systems (CS) used in this artile are shown in Figure 1 he referene is the world CS Σ he thigh CS Σ is fied at the middle of the ompromising rotation ais of the knee joint, whih is assu as the line between the femur ondyles When the leg is strethed (fleion angle ) the thigh ( Σ ) and the shank ( Σ S ) CS are mathed Leaned on ial terms the position of the shank relative to the thigh is ribed by three translations and three rotations as follows: First the shank is rotated around the ais by the angle ϕ (fleion-etension, fe) After that the shank is translated along the atual ais (ial-lateral) by the distane and y ais (anterior-posterior) by y Afterwards the leg is rotated around the atual y ais by the angle ψ (varus-valgus, VV) and around the atual z ais (internal-eternal) by ϑ At last the translation along the atual z ais (distal-proimal) is perfor by the distane z Note that the translations of the displaement ribed by the vetor ( y z ϕ ψ ϑ ) are not orthogonal As an (of ourse very theoretial) eample: a displaement of 5mm is the same than a displaement of z 5mm at a VV angle of ψ 9 Beause of this, the displaement ribed in ial oordinates is transfor to an orthogonal nial oordinate system ribed by

2 y z ϕ ψ ϑ + z sin( ψ y z os( ψ ) ϕ ψ ϑ ) y z ϕ ψ ϑ he position of the shank in nial oordinates is ribed by a rotation around the ais After that all translations, y and z are perfor At least the rotations ψ and ϑ around the atual ais eah time are perfor he sueeding rotations ribe Euler angles as introdued in [Siaviio] Synta Vetor ontaining transversal and rotatory displaements f Generalized fore vetor with 3 fores and 3 torques Medial lateral translation (ML) y Anterior posterior translation (AP) z Distal proimal translation (DP) ϕ Etension fleion rotation ( : strethed leg) (EF) ψ Varus valgus rotation (VV) ϑ Internal eternal rotation (IE) MEHODS he elasti aspets of a knee joint an be ribed by its stiffness that is the ontet between load and displaement: hange of fore or torque Stiffness hange of translatory or rotatory displaement s dfi( ) d i fi i ; i 16 o detet the stiffness of the knee joint s different degrees of freedom as they are ribed above, the hange of fores/torques as a funtion of the displaement has to be measured Setup he key element of the setup for detetion of the knee joint s stiffness is the high preision industrial robot Stäubli RX9- B It is apable to apply fores up to 1N and torques up to 1Nm he position auray is better than 1mm It is equipped with a pneumati safety devie (IPR GmbH) and a 6 DOF fore torque sensor (JR3 In) he bones of thigh and shank of the human adaver leg are sealed with epoy resin in tubes made of aluminum Additionally, there are three srews fiing the bones he tube with the thigh is mounted to a fied position at the fundament of the robot he shank is mounted to a plate that an be fied and dismantled within seonds to and from the fore torque sensor (Figure 2) he position of the adaver leg relative to the robot was hosen in that way that no singular onstellations of the robot ourred in the required work spae A robot singularity would redue the number of DOF of the robot s end effetor, so the robot annot move into all diretions in that onstellation [Siaviio] (1) Figure 2: Setup for measuring knee joint harateristis in 6 DOF Control hardware he original ontroller (Stäubli CS7-B) of the robot is not powerful enough he maimal possible sampling rate is 625 Hz for eah hannel his ontroller was used in the first setup for measuring knee joint harateristis he perfor measurements have been very slow and during the measurement of rather high stiffness osillations ourred In the seond setup, whih is presented in this work, the original ontroller was replaed by a Real ime Linu based one developed in our lab [Hoogen] It works on a Pentium IV with 19 MHz he interfae to the robot is realized with adequate PCI ards for the fore torque sensor, input of joint enoder values and voltage output ontrolling the urrent of the robot s joints his setup enables to inrease the sampling rate up to 4 khz for eah hannel Control strategy A hybrid losed loop fore torque position ontrol enables to drive eah DOF either position or fore ontrolled he simplified struture of the losed loop ontrol is shown in Figures 3 and 4 he input for eah hannel is either the ired fore/torque or the ired translational/rotational displaement depending on the hoie weather the DOF is fore/torque or position ontrolled he input is set in ial oordinates introdued above

3 veloities q& with the inverse Jaobian matri of the robot [Siaviio] q& and the robot joint onstellation q are the inputs of a robot joint subsidiary position veloity ontrol his lose loop ontrol is alulating the ired urrent for the robot joint motors he losed urrent ontrol loop is not displayed in figure 4 he atual robot joint onstellation q is a result of the dynamis of the robot and the atual urrents for the robot Figure 3: Simplified ontrol struture of the setup f C y 1 + z + ϕ y ψ ϑ ( E C) f f is the input vetor, z ϕ ψ ϑ f the ired position vetor, f the ired fore vetor, E is the identity matri and C the hoie matri By setting the i th diagonal element ii 1 position ontrol is hosen for the i th DOF, fore ontrol is hosen when ii he diagonal elements of the matri C are olleted in the vetor ( y z ϕ ψ ϑ ) (2) With equation (1) the input f is transfor to the orthogonal nial CS he result is error e is the ired input f he ontrol f minus the atual state f f is obtained by merging atual fores/torques and displaement as it is done with the input vetor: f C + ( E C) f he error e is the input of a p-ontroller that is adapted online by the atual fores and torques he output of the ontroller is a vetor of ired translatori and rotatori veloities & & is transfor to ired robot joint Figure 4: Control sheme for data aquisition VWL: forward kinematis of the robot onsidering the loation of the tool enter point FS: Fore torque sensor J: Jaobian Matri of the robot Figure 5: omparison of intat knee joint and knee joint

4 joint motors he robot ats to the human adaver leg and auses fores and torques that are measured with the fore torque sensor (FS) ransformation of the fores/torques to the nial oordinate system and ompensation of gravity fores and moments are not displayed in Figure 4 he atual displaement of the knee joint is alulated with the robot s kinematis (VWL) All the ribed steps are done 4 times per seond A user interfae has been developed for ontrolling the robot (Figure 6) With this menu-driven program it is possible to do all settings required for measuring knee joint harateristis his are the maimum fore/torque and the maimum and minimum displaements for eah DOF, the resolution to be measured, hoose of ontrol mode (position or fore/torque ontrolled), initialization data and other parameters Furthermore, it is possible to plot the measured data imiately after measurements have been perfor Initialization Before the start of measurements some initialization routines have to be driven he tool enter point of the robot has to be set to the middle of the ompromising rotation ais of the knee joint he tool enter point is the point where fores/torques are measured It influenes the VWL of the robot and the transformation /W (Figure 4) as well he line between the femoral epiondylar uberula is hosen as the ompromising rotation ais Until now the loation of this ais is done by manual measurements But an advaned initialization routine will be implemented using C data and a robot based loation of the bones soon Furthermore, estimation of the lower leg mass and the enter of mass is done for the use with the gravity ompensation routine inreasing the fleion angle position ontrolled from to 12 while all other DOF were zero fore ontrolled: ( 1 ), f ( ( 12 /1 ) ) Varus-valgus stiffness: For measuring VV stiffness all translatory DOF (PD, ML, AP) have been zero fore ontrolled he reorded information about the neutral position ϑ ( ϕ) of the IE rotation as a funtion of the fleion angle is used as an input for the position ontrolled IE rotation DOF he fleion angle is position ontrolled to a fi angle while VV torque varies between -1 and 1 Nm: ( 1 1), f ( ( 12 / 2 ) ( 11/1Nm) ϑ ( )) ϕ he knee joint is loaded alternately several times with the maimum and the minimum VV torque to avoid measuring fleion dependent hysteresis effets hen the fore is inreased and dereased up to ± 1Nm in steps of 2 Nm After that the fleion angle inreases to the net onstellation to be measured (Figure 7) his proedure was also done with the same adaver but ruptured ial ligament and both ruptured ial and lateral ligament As a result hysteresis urves like that ones in Figure 5 are obtained he single urves are shifted by a VV angle, so they are displayed one by eah other Proessing Zero internal-eternal rotation: At first zero internal eternal (IE) rotation ϑ ( ϕ) as a funtion of the fleion angle [Wilson] has been deteted his was done by Figure 6: user interfae for the setup

5 Figure 8: Hyperetesion as funtion of the fleion angle Figure 7: Varus-valgus load and fleion angle while measuring Fleion-etension stiffness: Measurements of hyperetension have been perfor with the same adaver knee joint herefore all DOF have been fore ontrolled he hyperetension fore has been inreased up to 8/1Nm in steps by 2 Nm while all other have been zero fore/torque ontrolled, f ( ( 1/ 2Nm) ) Figure 8 displays the reorded data for the intat knee, the knee joint with ruptured ial ligament and the knee joint with ruptured ial and lateral ligament Auray he auray of the setup was determined by fiing the mounting attahed to the fore torque sensor diret to an aluminium tube as it is used for fiing the thigh Fores and torques have been applied to the tube and displaement was measured he resulting transversal stiffness is at least 44kN/m up to 188kN/m depending on the robot s onstellation his stiffness orresponds to a displaement of 22mm and 5mm at a load of 1N he rotatory stiffness is between 22 Nm/ for fleion DOF and 4 Nm/ for IE rotation of the knee joint At the maimum load of 1 Nm this stiffness orresponds to a displaement of 45 and 25, respetively RESULS AND DISCUSSION he eperimental setup works very satisfatory and a lot of data ould be olleted from a single adaver All the measurements shown in able 1 have been perfor in less than one and a half hours time of work with the robot Beause of the high stiffness of the setup the measured positions are rather aurate he repetition auray is also very satisfying as there is only a slight differene between two sequened measurements Of ourse, there are some soures of errors that have to be onsidered For eample the manually done initialization routine is error-prone but when done arefully it works Furthermore, the preession is limited by the resolution of the fore sensor and the nonlinear stiffness harateristis of the robot With the implemented adaptive hybrid fore torque position ontrol it is possible to ontrol eah DOF either position or fore ontrolled Furthermore, any ombination of loads in different DOF is possible eg the detetion of VV stiffness as a funtion of the IE rotation torque and the fleion angle he data shown in Figure 8 indiate no ontribution of the ial or lateral ligament to hyperetension stiffness All reorded urves are nearly idential Valgus Varus stiffness (Nm/ ) Valgus Varus load (Nm) -5 fleion ( ) Intat Joint Detahed ial ligament Detahed ial and lateral ligament Figure 9: Valgus stiffness with various loads Figure 5 displays the varus-valgus torque as funtions of the varus-valgus angle of the intat and insured knee joint he urves for the different fleion angles are shifted to eah other with angle offsets he data indiate no ontribution of the ial ligament to varus harateristis for a varus load larger than 1 Nm 1 5 9

6 No Perfor measurements 1 Zero rotation as a funtion of fleion 2 Varus-valgus (VV) of the intat joint 3 VV with detahed ial ligament 4 VV with detahed and lat lig 5 Hyperetension 6 Hyp with detahed lig 7 Hyp with detahed and lat lig able 1: perfor measurements he varus stiffness has been alulated and is displayed in Figure 9 his was done with the data shown in Figure 5 Additional there is onsidered the stiffness with both ruptured ial and lateral ligament he stiffness urves for ruptured ial and that one for ruptured ial and lateral ligament are lose together for loads bigger than 1 Nm his indiates no ontribution of the lateral ligament to valgus stiffness for loads bigger than 1Nm OULOOK With the presented setup we obtained biomehanial data in 6 DOF with high data resolution In near future we are going to analyze ross oupling of more than two DOF, eg the stiffness of rotation as a funtion of VV load and fleion angle Furthermore, we are going to onsider other pathologies suh as ruptured anterior and posterior ruial ligament With an advaned method for initialization we will be able to obtain aurate data about the absolute position of thigh and shank he data obtained in this study will be used for the Munih Knee Joint Simulator [Riener], that requires a biomehanial model of the knee joint [Frey] REFERENCES Frey, M, et al (23) Varus valgus model of the knee identified by a robot based approah Pro ISB Congress 3 Fujie, H, et al (1993) J Bio Eng, 115, Fujie, H, et al (1995) J Bio Eng, 117, 1-7 Hoogen, J, et al (22) A roboti hapti interfae for kinaestheti knee joint simulation Pro Robotis in Alpe- Adria-Danube Region Hurshler, C et al (2) A nique for the measurement of musle moment arms during simulated ative elevation of the shoulder Pro 12 th Conf Europ So Biomeh, 163 Hurshler, C, et al (21) Am J Sports Med, 29(3), Moore,, et al (1976) J Bone & Joint Surg, 594 ff Neme, B, et al (2) he use of robotis nology for kinemati test of synovial joints in iine Pro 9 th International Workshop Riener, R, et al (23) IEEE rans Inform eh in Bio, submitted Siaviio, L, Siiliano, B (2) Modelling and Control of Robot Manipulators, London: Springer-Verlag Wilson, DR, et al (2): J Biomeh 33, Woo, SLY, et al (2) Pro Int Conf Bio Eng ACKNOWLEDGEMENS We thank Prof G Shmidt, J Hoogen, homas Pröll, Stefan Pelhak and Werner Mairegger for their support in this study his work was supported by German Ministry for Eduation and Researh within the projet network on Virtual Orthopedi Reality (VOR) (1IRA15)