SciELO - Scientific Electronic Library Online

vol.7 número3Binocular visual tracking and grasping of a moving object with a 3D trajectory predictor índice de autoresíndice de materiabúsqueda de artículos
Home Pagelista alfabética de revistas  

Servicios Personalizados




Links relacionados

  • No hay artículos similaresSimilares en SciELO


Journal of applied research and technology

versión On-line ISSN 2448-6736versión impresa ISSN 1665-6423

J. appl. res. technol vol.7 no.3 Ciudad de México dic. 2009


Jerk analysis of a module of an artificial spine by means of screw theory


J. Gallardo–Alvarado*, R. Lesso–Arroyo


Department of Mechanical Engineering, INSTITUTO TECNOLÓGICO DE CELAYA Av. Tecnológico y A. García Cubas, 38010 Celaya, GTO, México. *,



In this work, a novel parallel manipulator is introduced with the purpose of simulating the jerk analysis of the end of the spine. The displacement analysis is presented in a semi–closed form solution whereas the velocity, acceleration and jerk analyses are carried out by means of the theory of screws.

Keywords: Parallel manipulator, spine, screw theory, jerk analysis, kinematics.



En este trabajo se introduce un manipulador paralelo novedoso con el propósito de simular el análisis de pulso de la columna vertebral. El análisis de posición se presenta en forma semi cerrada, mientras que los análisis de velocidad, aceleración y pulso son realizados por medio de la teoría de tornillos.

Palabras clave: Predicción lineal, servo control visual, seguimiento, visión estéreo, calibración de cámaras.





[1] Morasso, P. Spatial control arm movements. Exp. Brain Res., Vol. 42, pp. 223–227 (1981).         [ Links ]

[2] Flash, T. and Hogan, N. The coordination of arm movements: an experimentally confirmed mathematical model. J. Neurosci., Vol. 5, pp. 1688–1703 (1985).         [ Links ]

[3] Uno, Y., Kawato, M., and Suzuki, R. Formation and control of optimal trajectory in human multijoint arm movements. Biol. Cybern., Vol. 61, pp. 89–101 (1989).         [ Links ]

[4] Crossman, E. R. F.W. and Goodeve, P. J. Feedback control of handmovements and Fitts law. Q. J. Exp. Psychol., Vol. A35, pp. 251–278 (1983).         [ Links ]

[5] Gielen, C. C., Vrijenhock, E. J., and Neggers, S. F. Arm position constraints during pointing and reaching in 3–D space. J. Neurophysiol., Vol. 78, pp. 660–673 (1997).         [ Links ]

[6] Goldvasser, D., McGibbon, C. A., and Krebs, D. E. High curvature and jerk analyses of arm ataxia. Biol. Cybern., Vol. 84, pp. 85–90 (2001).         [ Links ]

[7] Novàk, K.E., Miller, L.E., and Houk, J. C. Kinematic properties of rapid hand movements in a knob turning task. Exp. Brain Res., Vol. 132, pp. 419–433 (2000).         [ Links ]

[8] Viviani, P. and Schneider, R. A. development study of the relationship between geometry and kinematics in drawing movements. J. Exp. Psychol. Hum. Percept. Perform., Vol. 17, pp. 198–218 (1991).         [ Links ]

[9] Viviani, P. and Flash, T. Minimum–jerk, two–thirds power law, and isochrony: converging approaches tomovement planning. J. Exp. Psychol. Hum. Percept. Perform., Vol. 21, pp. 32–53 (1995).         [ Links ]

[10] Panjabi, M.M., White, A.A. Basic biomechanics of the spine. Neurosurgery, Vol. 7, pp. 76–93 (1980).         [ Links ]

[11] Dimnet, J., Pasquet, A., Krag, M.H., Panjabi, M.M. Cervical spine motion in the sagittal plane: Kinematic and geometric parameters. Journal of Biomechanics, Vol. 15, pp. 959–969 (1982).         [ Links ]

[12] Gracovetsky, S., Farfan, H. The optimum spine. Spine, Vol. 11, pp. 543 (1986).         [ Links ]

[13] Cholewicki, J., McGill, S.M. Lumbar spine kinematics obtained from videofluoroscopy. Journal of Biomechanics, Vol. 25, pp. 801 (1992).         [ Links ]

[14] Yoganandan, N., Pintar, F., Maiman, D. J., Reinartz, J., Sances, A., Larson, S.J., Cusick, J.F. Kinematics of the lumbar spine following pedicle screw plate fixation. Spine, Vol. 18, pp. 504–512 (1993).         [ Links ]

[15] Levin, S.M. The importance of soft tissue for structural support of the body. In Dorman, T.A., editor. Prolotherapy in the lumbar spine and pelvis, Spine: State of the art reviews, Vol. 9, pp. 357 (1995).         [ Links ]

[16] Willems J.M., Jull G.A., Ng, J.K.–F. An in vivo study of the primary and coupled rotations of the thoracic spine. Clinical Biomechanics, Vol. 11, pp. 311–316 (1996).         [ Links ]

[17] Faber, M.J., Schamhardt, H.C., van Weeren, P.R. Determination of 3D spinal kinematics without defining a local vertebral coordinate system. Journal of Biomechanics, Vol. 32, pp. 1355–1358 (1999).         [ Links ]

[18] Yoshikawa, H., Ishii, T., Mukai, Y., Hosono, N., Sakaura, H., Nakajima, Y., Sato, Y., Sugamoto, K. Kinematics of the upper cervical spine in rotation: In vivo three–dimensional analysis. Spine, Vol. 29, pp. E139–E144 (2004).         [ Links ]

[19] Ziddiqui, M., Karadimas, E., Nicol, M., Smith, F.W., Wardlaw, D. Effects of X–stop device on sagittal lumbar spine kinematics in spinal stenosis. Journal of Spinal Disorden Technology, Vol. 19, pp. 328–333 (2006).         [ Links ]

[20] Ishii, T., Mukai, Y., Hosono, N., Sakaura, H., Fujii, R., Nakajima, Y., Tamura, S., Iwasaki, M., Yoshikawa, H., Sugamoto, K. Kinematics of the cervical spine in lateral bending: In vivo three–dimensional analysis. Spine, Vol. 31, pp. 155–160 (2006).         [ Links ]

[21] Konz, R.J., Fatone, S., Stine, R.L., Ganju, A., Gard, S.A., Ondra, S.L. A kinematic model to assess spinal motion during walking. Spine, Vol. 31, pp. E898–E906 (2006).         [ Links ]

[22] Chanceya, V.C., Ottaviano, D., Myers, B.S., Nightingale, R.W. A kinematic and anthropometric study of the upper cervical spine and the occipital condyles. Journal of Biomechanics, Vol. 40, pp. 1953–1959 (2007).         [ Links ]

[23] Gill, K.P., Bennett, S.J., Savelsbergh, G.J.P., van Dieèn, J.H. Spine, Vol. 32, pp. 1599–1604 (2007).         [ Links ]

[24] Jones, M., Holt, C., Franyuti, D. Developing a methodology for the analysis of infant spine kinematics for the investigation of the shaken baby syndrome. Journal of Biomechanics, Vol. 41, pp. S3–55 (2008).         [ Links ]

[25] Zhu, S.J., Huang, Z., Zhao, M.Y. Feasible Human–Spine Motion Simulators Based on Parallel Manipulators Source: Parallel Manipulators, Towards New Applications, Book edited by: Huapeng Wu, ISBN 978–3902613–40–0, pp. 506, I–Tech Education and Publishing, Vienna, Austria (2008).         [ Links ]

[26] Innocenti, C, Parenti–Castelli, V. Direct position analysis of the Stewart platform mechanism. Mechanism and Machine Theory, Vol. 35, pp. 611–621 (1990).         [ Links ]

[27] Tsai, L.–W. Robot analysis, John Wiley & Sons, (1999).         [ Links ]

[28] Gallardo–Alvarado, J., Rodríguez–Castro, R., Nazrul Islam, Md. Analytical solution of the forward position analysis of parallel manipulators that generate 3–RS structures. Advanced Robotics, Vol. 22, pp. 215–234 (2008ª         [ Links ]).

[29] Gallardo–Alvarado, J., Aguilar–Nájera, C.R., Casique–Rosas, L., Pérez– González, L., Rico–Martínez, J.M. Solving the kinematics and dynamics of a modular spatial hyper–redundant manipulator by means of screw theory. Multibody System Dynamics, Vol. 20, pp. 307–325 (2008b).         [ Links ]

[30] Ball, R.S. A Treatise on the Theory of Screws, Cambridge University Press: Cambridge. 1900 (reprinted 1998).         [ Links ]

[31] Rico, J.M., Duffy, J. An Application of screw algebra to the acceleration analysis of serial chains. Mechanism and Machine Theory, Vol. 31, pp. 445–457 (1996).         [ Links ]

[31] Rico, J.M., Duffy, J. An Application of screw algebra to the acceleration analysis of serial chains. Mechanism and Machine Theory, Vol. 31, pp. 445–457 (1996).         [ Links ]

[32] Gallardo–Alvarado, J., Orozco–Mendoza, H., Rodríguez–Castro, R. Finding the jerk properties of multi–body systems using helicoidal vector fields. Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science, Vol. 222, pp. 2217–2229 (2008c).         [ Links ]

Creative Commons License Todo el contenido de esta revista, excepto dónde está identificado, está bajo una Licencia Creative Commons