THE HUMAN FEMUR MOTION AND TORQUE IN HIP JOINT

Transcription

1 HE HUMAN FEMUR MOION AND ORQUE IN HIP JOIN D. Drăguleu*, L. Ruu**, H. Moldovan *** Abtrat Normal human loomotion require a omplex interative ontrol between multiple limb and body egment that work ongruently to provide the mot hok-aborbing and energy-eiient orward movement poible. he kinemati model onider the hip joint a a uperpoition o independent, orthogonal and imple revolute joint and the knee joint a a imple revolute one. Conerning dynami model, the tudy aim wa to repreent the ative ore and moment needed in joint in order to aure the motion by onidering the role o mule at every phae, a well a the human leg ma ditribution. Key Word: Femur, joint, kinemati.. Introdution he paper tudie the emur bone a a part o human lower limb. Conerning kinemati model, the human emur i onidered a an artiulated body between the hip joint and the knee one. he kinemati modeling wa perormed by uing Denavit-Hartenberg roboti onvention. he dynami behavior tudy ollowed to etimate the torque in hip joint. For that, the original Bio&Sot program wa reated whih i able to ompute all ore and moment in the human loomotor apparatu joint.. Motion modeling he kinemati model onider the hip joint a a uperpoition o independent, orthogonal and imple revolute joint and the knee joint a a imple revolute one (igure ). hi model i onordant with anatomi knowledge about dierent poible motion inide emur human joint. * Politehnia Univerity o imioara ddrag@.utt.ro ** Politehnia Univerity o imioara luk@mpiu.utt.ro *** Politehnia Univerity o imioara

2 Fig.. Kinemati emur model Denavit-Hartenberg onvention wa applied and, a a reult, the able wa obtained and the orrepondent traner matrie too: able Joint q i α i l i d i o in in o o in in o o in in o in o in o in o () where: i (i,,) are joint variable and i the emur length. he kinemati equation, deribing emur motion with repet to the general reerene rame, are given by multiplying the traner matrie (). So, the general matrix:

3 ) ( ) ( ) ( ) ( ) ( ) ( ) ( G () where there were noted:,, in o K i i i i i. he kinemati equation were written in order to model the emur lower extremity motion (into knee joint) with repet to the ixed reerene rame. By onidering a medium ize emur 5 m o length and impoing the anatomi limitation to angle, and, the global diplaement o the origin o x O y z wa alulated with repet to the origin o the ixed reerene rame (igure ). y -6E-7x 5 7E-5x -.7x.x -.569x ime [] Lower extermity emur diplaement [m] Fig.. Lower extremity emur diplaement onormably to the kinemati model here were ued the value o the expreion in the lat olumn o general matrix () or the irt quarter o a pae (the emur motion rom the vertial poition to orward). For the eond quarter o the pae (the emur motion rom extreme orward poition during walking, to the vertial one) the urve will be ymmetrial with repet to the vertial paing through the value o 8 (igure ). For the two lat quarter o the pae, the urve will be ymmetrial with repet to the vertial axi paing through the value o 56. It i repreented in igure even the analytial untion modeling the urve deribed by the lower extremity o the emur during the irt quarter o the walking pae. It wa repreented by uing the R-quared value o,69.

4 Fig. Lower extremity emur motion during a hal walking pae For the other part o the walking pae, the analytial untion modeling the urve ould be etimated on the ame way.. Dynami torque in hip joint Conerning dynami model, the tudy aim wa to repreent the ative ore and moment needed in joint in order to aure the motion by onidering the role o mule at every phae, a well a the human leg ma ditribution. Fig. Generalized ore (moment) moving the emur around O z axi he reated Bio&Sot program, reated in Viual Bai., wa ued to ompute the ore at eah pae phae, a untion o magnitude, inert point poition and diretion o mule. By reduing thee ore with repet to the reerene rame plaed in eah joint, the ative torque in joint were obtained. A impliied model o human lower limb wa adopted [] and or thi one, by uing nd degree Lagrange equation the generalized ore (moment) in joint were alulated. For example, in igure it i repreented an image apture o Bio&Sot dynami analyze the ative moment Q turning the emur around the O z axi in the hip joint. It wa omputed by uing the th degree Lagrange equation ytem, written or the emur a a rigid body in igure. By ombining, a a vetorial um, the three moment ating in hip joint, the graphial repreentation o the reultant moment o three orthogonal one i obtained in igure 5.

5 Fig.5 Reultant moment in hip joint during a walking pae he numerial value got by uing Bio&Sot were plotted by uing MatLab a ollow: x [ ]; y [ ]; polyit(x,y,7); x :.:.75; y polyval(,x); plot(x,y,x,y);. Conluion Normal human loomotion require a omplex interative ontrol between multiple limb and body egment that work ongruently to provide the mot hok-aborbing and energy-eiient orward movement poible. Gait harateriti are inluened by mule trength, dynami range o motion, and hape, poition and untion o numerou neuromuular and muulokeletal truture, a well a, the ligamentou and apular ontraint o the joint. he primary goal i energy eiieny in progreion uing a table kineti hain o joint and limb egment that work ongruently to tranport the paenger unit orward. Clearly, or a imple mehanim uh a the RR arm, uing DH i a big overhead a ompared to imple trigonometry. But or omplex mehanim, DH i ar eaier to automate. Alo, one the rame are ixed and the parameter identiied, it i eay to ind the relationhip between any two rame on the mehanim. Alo, the DH parameter are an eay way o ompletely peiying the mehanim. We will ee more o DH in uture lae. 5

6 5. Reerene [] Doina Draguleu, Mirela oth aau, Dan Staniu: Kinemati and Dynami Modeling o Human Lower Limb IASED International Conerene Roboti and Apliation Nov. 9-, ampa Florida USA p. -7; [] Gage, J.R.: An Overview o Normal Walking AAOS Intrutional Coure Leture 99; Vol 9; Chapter 7:9-; [] Goldberg, K., Halperin, D., Latombe, J., et al. (Ed.): he Algorithmi Foundation o Roboti (A. K. Peter, Boton, MA, 995); [] Greene W.B. and Heknman J.D.: he Clinial Meaurement o Joint Motion Amerian Aademy o Orthopaedi Surgeon, Roemont, Illinoi, 97-, 99; [5] J.J. Crary, "Introdution to Roboti: Mehani and Control", Addion Weley Reading MA, 986; [6] Jaramaz B., et al.: Simulation o implant impingement and diloation in total hip replaement CAR 96, th international ympoium and exhibition, Pari, June 6-9, 996; [7] Johnton, R.C. and Smidt, G.L.: Hip motion meaurement or eleted ativitie o daily living Clin.Orthop. Sept-Ot 97; (7): 5-5; [8] Pauwel F Biomehani o the Loomotor Apparatu Berlin Heidelberg New York: Springer-Verlag; [9] Van Eijden,.M.G., Kouwenhoven, E., Verburg, J., and Weij, W.A. (986), "A Mathematial Model o the Patelloemoral Joint", Journal o Biomehani,,