Two-Dimensional kinematics of horses at trot through videometry and mathematical modeling




Angular kinematics, Horse locomotion, Inverse kinematics, Mathematical model, Videometry


Currently, the direct observation method is used to assess the movement of horses; however, this method is limited, totally subjective, and many details of the musculoskeletal system functionality cannot be detected and evaluated because they are not perceptible to the naked eye. This study aimed at developing a mathematical model that calculates, plots, and simulates the 2D angular movement of some horse joints. The horse musculoskeletal system was modeled as a mechanical system of rigid bodies articulated by 15 simple joints. The mathematical solution of the mechanism was obtained from the standpoint of inverse kinematics (flat) liabilities. We constructed 15 link equations, associating the body segments of the system in movement with an inertia base, and used the mathematical optimization method based on the least squares calculation. We obtained kinematic curves of the main joints, as well as the trajectories (height) of the markers on fore and hind coronary band (hoofs), and a simulation of the mechanical system. This tool removes subjectivity and enables veterinarians to observe, evaluate (qualitatively and quantitatively), diagnose, and investigate different phenomena of the horse gait.


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A. Vukolov, A. Golovin, and N. Umnov, “Horse Gait Exploration on Step, Allure by Results of High Speed Strobe light Photography,” in Symposium a Quarterly Journal in Modern Foreign Literatures, pp. 361-368, 2010. DOI:

M. Valera, A. Molina, and F. Goyache, “Assessment of inbreeding depression for body measurements in Spanish Purebred (Andalusian) horses,” Livestock Science, vol. 122, pp. 149-155, 2008. DOI:

M. C. Hilary, and H. C. Schamhardt, “Measurement Techniques for Gait Analysis,” in Equine Locomotion, Ed. W.B. Saunders, London, pp 55-76, 2000.

I. D. Wijnberg, J. Sleutjens, J. H. Van Der Kolk, and W. Back, “Effect of head and neck position on outcome of quantitative neuromuscular diagnostic techniques in Warmblood riding horses directly following moderate exercise,” Equine Vet. J., vol. 42, pp. 261-267, Nov. 2010. DOI: DOI:

C. Degueurce, H. Chateaua, V. Pasqui-Boutardb, P. Pourcelota, F. Audigiéa, N. Crevier-Denoixa, H. Jerbia, D. Geigerc, and J.-M. Denoix, “Concrete use of the joint coordinate system for the quantification of articular rotations in the digital joints of the horse,” Veterinary Research, vol. 31 (3), pp. 297-311, May. 2000. DOI: DOI:

L. Raghunandana, “Development and validation of biomechanical models to quantify horseback forces at the walk in three horse breeds,” Thesis (Master of Science in Electrical Engineering), Louisiana State University, Department of Electrical and Computer Engineering, 2011.

V. D. Bogert, H. C. Schamhardt, and A. Crowe, “Simulation of quadrupedal locomotion using a rigid body model,” J. Biomech., vol. 22 (1), pp. 33-41, Jan. 1989. DOI: DOI:

M. De Souza, “Influence of camped under associated with upright pastern in front conformation in the forelimb movement of horses,” J. of Equine Vet. Sci., vol. 24 (8), pp. 341-346, Aug. 2004. DOI: DOI:

A. Galisteo, and R. Vivo, “Patrón locomotor del trote del caballo Pura Raza Español y su variabilidad,” RECVET- Revista Electrónica de Clínica Veterinaria, vol. III, pp. 1-17, 2008.

A. Molina, M. Valera, A.M. Galisteo, J. Vivo, M.D. Gómez, A. Rodero, and E. Agüera, “Genetic parameters of biokinematic variables at walk in the Spanish Purebred (Andalusian) horse using experimental treadmill records,” Livestock Science, vol. 116 (1-3), pp. 137-145, Jul. 2008. DOI: DOI:

M. R. Cano, J. Vivo, F. Miró, J. L. Morales, and A. M. Galisteo, “Kinematic characteristics of Andalusian, Arabian and Anglo-Arabian horses: a comparative study,” Res. Vet. Sci., vol. 71 (2), pp. 147-153, Oct. 2001. DOI: DOI:

H. M. Clayton, “Comparison of the stride kinematics of the collected, working, medium and extended trot in horses,” Equine Vet. J., vol. 26 (3), pp. 230-234, May. 1994. DOI: DOI:

A. M. Galisteo, M. R. Cano, J. L. Morales, J. Vivo, and F. Miró, “The influence of speed and height at the withers on the kinematics of sound horses at the hand-led trot,” Vet. Res. Commun., vol. 22 (6), pp. 415-423, 1998. DOI: DOI:

E. Barrey, B. Landjerit, and R. Wolter, “Shock and Vibration during the hoof impact on different track surfaces,” Equine Exerc. Physiol., no. 3, pp. 97-106, 1991.

H. M. Clayton, D. H. Sha, J. A. Stick, and P. Robinson, “3D kinematics of the interphalangeal joints in the forelimb of walking and trotting horses,” Vet. Comp. Orthop. Traumatol., vol. 20 (1), pp. 1-7, 2007. DOI:

H. M. Clayton, D. Sha, J. Stick, and N. Elvin, “3D kinematics of the equine metacarpophalangeal joint at walk and trot,” Vet. Comp. Orthop. Traumatol., vol. 20 (2), pp. 86-91, 2007. DOI: DOI:

Y. Torres-Pérez, E. Y. Gómez-Pachón, F. Cuenca-Jiménez, “Horse’s gait motion analysis based on videometry,” Rev. Cien. Agri., vol. 13 (2), pp. 83-94, 2016. DOI:

Y. Torres-Pérez, F. Cuenca, and A. Ortiz, “Cinemática articular 2D de un caballo durante marcha normal,” SOMIM, pp. 948-956, 2011.

Y. Torres-Pérez, O. Jiménez, and A. Ortiz, “Generated Graphical Interface Design of the Normality Bands of the 2D Equine Kinematics,” Revista Argentina de Bioingeniería. vol. 20, no. (1), pp. 39-42, 2014.

F. Miró, J. Vivo, R. Cano, A. Diz, and A. M. Galisteo, “Walk and trot in the horse at driving: kinematic adaptation of its natural gaits,” Anim. Res., vol. 55 (6), pp. 603-613, Nov. 2006. DOI: DOI:

R. C. Hibbler, “Dinámica – Mecánica para ingeniería,” Prentice Hall, Ciudad de México, 2004.

M.J.D. Powell, “A method for minimizing a sum of squares of non-linear functions without calculating derivatives,” Comput. J., vol. 7 (4), pp. 303-307, 1965. DOI: DOI:

R. Fletcher, “Function minimization without evaluating derivatives a review,” Comput. J., vol. 8 (1), pp. 33-41, 1965. DOI: DOI:

A. Byström, M. Rhodin, K. Peinen, M. A. Weishaupt, and L. Roepstor, “Basic kinematics of the saddle and rider in high-level dressage horses trotting on a treadmill,” Equine Vet. J., vol. 41 (3), pp. 280-284, Mar. 2009. DOI: DOI:

A. Veinguertener, T. Hoinville, O. Bruneau, and J. Fontaine, “Two-Legged Animals to the HexaQuaBip Robots Reconfigurable Kinematics,” in ICIRA, pp. 1255-1265, 2009. DOI:

C. Y. Li, H. T. Gao, Y. B. Ma, C. Liu, and H. Wang, “Artificial Horse for Rehabilitation,” Springer-Verlag Berlin Heidelberg, no. 19, pp. 497-499, 2008. DOI:

M. Walter, and C. G. Franco, “Fast Customization of Geometric Models,” IEEE, pp. 146-151, 2000. DOI: DOI:

L. Reveret, L. Favreau, C. Depraz, and M. P. Cani, “Morphable model of quadrupeds skeletons for animating 3D animals,” in Symposium on Computer Animation, pp. 135-142, 2005. DOI: DOI:

E. Boxerman, Dynamic Model of a Horse Gallop in 2D, Available:

L. Skrba, L. Reveret, F. Hétroy, M.-P. Cani, and C. O'Sullivan, “Animating Quadrupeds: Methods and Applications,” Computer Graphics Forum, vol. 28 (6), pp. 1541-1560, Sep. 2009. DOI: DOI:

A. M. Galisteo, M. R. Cano, J. L. Morales, F. Miró, J. Vivo, and E. Agüera, “Kinematics in horses at the trot before and after an induced forelimb supporting lameness,” Equine Vet. J. Suppl., vol. 29 (S23), pp. 97-101, 1997. DOI: DOI:




How to Cite

Torres-Pérez, Y., Gómez-Pachón, E. Y., & Miró-Rodriguez, F. (2017). Two-Dimensional kinematics of horses at trot through videometry and mathematical modeling. Revista Facultad De Ingeniería, 26(45), 83–96.