Abstract
The paper presents a theoretical model of the ankle joint, i.e. tibio-talar articulation, which shows how the articular surfaces and the ligaments, acting together as a mechanism, can control the passive kinematics of the joint. The authors had previously shown that, in virtually unloaded conditions, the ankle behaves as a single degree-of-freedom system, and that two ligament fibres remain nearly isometric throughout the flexion arc. Two different equivalent spatial parallel mechanisms together with corresponding kinematic models were formulated. These assumed isometricity of fibres within the calcaneal-fibular and tibio-calcaneal ligaments and rigidity of the articulating surfaces, taken as three sphere-plane contacts in one model, and as a single spherical pair in the other. Geometry parameters for the models were obtained from three specimens. Motion predictions compare quite well with the measured motion of the specimens. The differences are accounted for by the simplifications adopted to represent the complex anatomical structures, and might be reduced by future more realistic representations of the natural articular surfaces.
Similar content being viewed by others
References
Alfaro-Adrian J, Gill HS, Murray DW (1999) Cement migration after THR. A comparison of Charnley and Exeter femoral stems with RSA. J Bone Joint Surg 81-B:130–134
Blankevoort L, Huiskes R (1991) Ligament–bone interaction in a 3-dimensional model of the knee. ASME J Biomech Eng 113(3):263–269
Cappozzo A, Catani F, Croce U, Leardini A (1995) Position and orientation in space bones during movement: anatomical frame definition and determination. Clin Biomech 10(4):171–178
Corazza F, O’Connor JJ, Leardini A, Parenti-Castelli V (2003) Ligament fibre recruitment and forces for the anterior drawer test at the human ankle joint. J Biomech 36:363–372
Corazza F, Stagni R, Parenti Castelli V, Leardini A (2005) Articular contact at the tibiotalar joint in passive flexion. J Biomech 38:1205–1212
Di Gregorio R, Parenti-Castelli V (2003) A spatial mechanism with higher pairs for modelling the human knee joint. ASME J Biomech Eng 125(2):232–237
Dul J, Johnson GE (1985) A kinematic model of the ankle joint. J Biomed Eng 7:137–143
Feikes JD (1999) The mobility and stability of the human knee joint. DPhil Thesis, University of Oxford, Oxford
Feikes JD, O’Connor JJ, Zavatsky AB (2003) A constraint-based approach to modelling the mobility of the human knee joint. J Biomech 36(1):125–129
Flaherty B, Robinson C, Agarwal G (1995) Identification of nonlinear model of ankle joint dynamics during electrical stimulation of soleus. Med Biol Eng Comput 33(3 Spec No):430–439
Giacomozzi C, Cesinaro S, Basile F, De Angelis G, Giansanti D, Maccioni G, Masci E, Panella A, Paolizzi M, Torre M, Valentini P, Macellari V (2003) Measurement device for ankle joint kinematic and dynamic characterisation. Med Biol Eng Comput 41(4):486–493
Giannini S, Corazza F, Leardini A, Parenti-Castelli V (2004) Biomeccanica dell’instabilità della tibiotarsica. Giornale Italiano di Ortopedia e Traumatologia, Suppl. 2 XXIX:86–97
Grood ES, Suntay WJ (1983) A joint coordinate system for the clinical description of three-dimensional motions: application to the knee. ASME J Biomech Eng 105:136–144
Hanson R, Norris M (1981) Analysis of measurements based on the singular value decomposition. SIAM J Sci Stat Comput 2:363–373
Hintermann B, Valderrabano V (2003) Total ankle replacement. Foot Ankle Clin 8:375–405
Innocenti C, Parenti-Castelli V (1993) Closed form direct position analysis of a 5–5 parallel mechanism. ASME J Mech Design 115:515–521
Innocenti C, Parenti-Castelli V (1993) Echelon form solution of direct kinematics for the general fully-parallel spherical wrist. Mech Mach Theory 28(4):553–561
Isman RE, Inman VT (1969) Anthropometric studies of the human foot and ankle. Bull Pros Res 10–11:97–129
Kerkhoffs GM, Struijs PA, Marti RK, Blankevoort L, Assendelft WJ, van Dijk CN (2003) Functional treatments for acute ruptures of the lateral ankle ligament: a systematic review. Acta Orthop Scan 74(1):69–77
Leardini A, O’Connor JJ, Catani F, Giannini S (1999) Kinematics of the human ankle complex in passive flexion: a single degree of freedom system. J Biomech 32:111–118
Leardini A, O’Connor JJ, Catani F, Giannini S (1999) A geometric model of the human ankle joint. J Biomech 32:585–591
Leardini A, O’Connor JJ, Catani F, Giannini S (2000) The role of the passive structures in the mobility and stability of the human ankle joint: a literature review. Foot Ankle Int 21(7):602–615
Leardini A, Stagni R, O’Connor JJ (2001) Mobility of the subtalar joint in the intact ankle complex. J Biomech 34(6):805–809
Leardini A, Catani F, Giannini S, O’Connor JJ (2001) Computer-assisted design of the sagittal shapes for a novel total ankle replacement. Med Biol Eng Comp 39(2):168–175
Leardini A, Moschella D (2002) Dynamic simulation of the natural and replaced human ankle joint. Med Biol Eng Comput 40(2):193–199
Leardini A, O’Connor JJ, Catani F, Giannini S (2004) Mobility of the human ankle and the design of total ankle replacement. Clin Orthop Rel Res 424:39–46
Lundberg A, Svensson OK, Nemeth G, Selvik G (1989) The axis of rotation of the ankle joint. J Bone Joint Surg Br 71(1):94–99
O’Connor JJ, Lu TW, Feikes J, Leardini A (1998) Diarthrodial joints: kinematic pairs, mechanical or flexible structures? Comp Meth Biomech Biomed Eng 1:123–150
Parenti-Castelli V, Di Gregorio R (2000) Parallel mechanisms applied to the human knee passive motion simulation. In: Lenarcic J, Stanisic M (eds) Advances in robot kinematics. Kluwer, Dordrecht. ISBN 0–7923–6426–0,333–344
Parenti-Castelli V, Leardini A, Di Gregorio R, O’Connor JJ (2004) On the modeling of passive motion of the human knee joint by means of equivalent planar and spatial parallel mechanisms. Auton Robots 16(2):219–232
Procter P, Paul JP (1982) Ankle joints biomechanics. J Biomech 15:627–634
Reggiani B, Leardini A, Corazza F, Taylor M (2006) Finite element analysis of a total ankle replacement during the stance phase of gait. J Biomech 39(8):1435–1443
Saltzman CL, McIff TE, Buckwalter JA, Brown TD (2000) Total ankle replacement revisited. J Orthop Sports Phys Ther 30:56–67
Stagni R, Leardini A, O’Connor JJ, Giannini S (2003) Role of passive structures in the mobility and stability of the human subtalar joint: a literature review. Foot Ankle Int 24(5):402–409
Stagni R, Leardini A, Ensini A (2004) Ligament fibre recruitment at the human ankle joint complex in passive flexion. J Biomech 37(12):1823–1829
Stauffer RN, Chao EYS, Brewster RC (1977) Force and motion analysis of the normal, diseased, and prosthetic ankle joint. Clin Orthop Rel Res 127:189–196
Wilson DR, Feikes JD, O’Connor JJ (1998) Ligament and articular contact guide passive knee flexion. J Biomech 31:1127–1136
Wilson DR, Feikes JD, O’Connor JJ (2000) The components of passive knee movement are coupled to flexion angle. J Biomech 33:465–73
Zwipp H, Rammelt S, Grass R (2002) Ligamentous injuries about the ankle and subtalar joints. Clin Pod Med Surg 19(2):195–229
Acknowledgments
The financial support of the Italian MIUR and CNR is gratefully acknowledged.
Author information
Authors and Affiliations
Corresponding author
Appendix
Appendix
Table 1
Rights and permissions
About this article
Cite this article
Di Gregorio, R., Parenti-Castelli, V., O’Connor, J.J. et al. Mathematical models of passive motion at the human ankle joint by equivalent spatial parallel mechanisms. Med Bio Eng Comput 45, 305–313 (2007). https://doi.org/10.1007/s11517-007-0160-7
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11517-007-0160-7