View Full Version : Minimal-Jerk Theory: lack of application to multi-joint systems and injury prevention

04-09-2011, 02:55 PM
In my interest of exploring the application of the minimal jerk theory to injury prevention, a colleague advised me on a study by Young & Marteniuk (1997) who measured root-mean-square jerk at the hip, knee and ankle during a weighted kicking movement. The premise they were working with is that although minimal jerk had been observed during one & two-joint discrete movements, the application of minimal jerk to multi-joint systems needed to be explored. These authors hypothesized that if minimal jerk is noted at the joint rather than the end-effort during multi-joint movements, this would support minimal-jerk theory and its possible role in preventing musculoskeletal injury. Their results showed that RMS-jerk & peak-jerk values at the hip, knee and ankle were all increased when a comparison was made between early and later trials blocks. Thus, the authors believed that since multi-joint movements became less smooth and peak jerk increased with learning, this made it doubtful that minimal jerk prevents injjury and challenge the application of the minimal-jerk model beyond two-joint kinetic systems. I would appreciate opinions or additional information. Thanks!

04-10-2011, 01:54 PM
Minimum jerk theory is a theory of endpoint movement related with task constraints, not of joint movements. It has been applied successfully on multi-joint movements (in the original paper by Flash & Hogan, 1985) and more complex tasks such as grasping (Smeets & Brenner, 1999). Following the theory, these papers do not deal with the movements of the joints, only the end-effector. An optimization of endpoint precision (given signal-dependent noise in muscles and mechanical properties of the limb) might be on the basis of the minimum jerk behavior (Harris & Wolpert, 1998). There are authors who have argued that there should be a simple cause at the joint level (minimum torque change model; Uno et al., 1989), but this model has never become very popular.

Flash, T., & Hogan, N. (1985). The coordination of arm movements: an experimentally confirmed mathematical model. Journal of Neuroscience, 5, 1688-1703.
Harris, C. M., & Wolpert, D. M. (1998). Signal-dependent noise determines motor planning. Nature, 394, 780-784.
Smeets, J. B. J., & Brenner, E. (1999). A new view on grasping. Motor Control, 3(3), 237-271.
Uno, Y., Kawato, M., & Suzuki, R. (1989). Formation and Control of Optimal Trajectory in Human Multijoint Arm Movement - Minimum Torque-Change Model. Biological Cybernetics, 61(2), 89-101.

04-13-2011, 01:18 PM
Hi Dennis,

I'm not terribly familiar with the theory, although Jeroen is correct, Flash & Hogan's "minimum jerk" was not formulated specifically to explain angular joint motions. Theories on the control of joint motion or whole-body motion have more often been related to the minimization of kinetic or metabolic quantities. If you're interested in injuries there is a large volume of literature that has suggested a relationship between loading rate (which would seem to be an analog of jerk; rate of change in force) and injuries (refs below). There's also a ton of literature on loading/strain rate and its effects on tissue damage in bone, muscle, tendon, etc.

Movement Control:
Ackermann M and van den Bogert AJ (2010). Optimality principles for model-based prediction of human gait. Journal of Biomechanics 43, 1055-1060.

Chow CK and Jacobson DH (1971). Studies of human locomotion via optimal programming. Mathematical Biosciences 10, 239-306.

Crowninshield RD and Brand RA (1981). A physiologically based criterion of muscle force prediction in locomotion. Journal of Biomechanics 14, 793-801.

Högberg P (1952). How do stride length and stride frequency influence the energy-output during running? European Journal of Applied Physiology 14, 437-441.

Hunter LC, Hendrix EC, and Dean JC (2010). The cost of walking downhill: is the preferred gait energetically optimal? Journal of Biomechanics 43, 1910-1915.

Kistemaker DA, Wong JD, and Gribble PL (2010). The central nervous system does not minimize energy cost in arm movements. Journal of Neurophysiology 104, 2985-2994.

Nubar Y and Contini R (1961). A minimal principle in biomechanics. Bulletin of Mathematical Biophysics 23 377-391.

Ralston HJ (1958). Energy-speed relation and optimal speed during level walking. European Journal of Applied Physiology 17, 277-283.

Sparrow WA and Newell KM (1998). Metabolic energy expenditure and the regulation of movement economy. Psychonomic Bulletin and Review 5, 173-196.

Loading Rate:
Hamill J, Miller RH, Noehren B, and Davis IS (2008). A prospective study of iliotibial band strain in runners. Clinical Biomechanics 23, 1018-1025.

Hreljac A, Marshall RN, and Hume PA (2000). Evaluation of lower extremity overuse injury potential in runners. Medicine and Science in Sports and Exercise 32, 1635-1641.

Milner CE, Ferber R, Pollard CD, Hamill J, and Davis IS (2006). Biomechanical factors associated with tibial stress fracture in female runners. Medicine and Science in Sports and Exercise 38, 323-328.

04-14-2011, 11:56 AM
Thank you Dr. Smeets and Dr. Miller for responding to my post and for correcting my misunderstanding of minimal jerk theory, namely, that it applies to end-effector coordinates and not angular displacement. I'm also grateful fot the references you provided, and for introducing me to the principle of minimization of kinetic quanties. As a new student to the field of biomechanics, this is why I believe BIOMCH-L is such a valuable information resource.
I would appreciate further clarification as to why Young & Marteniuk (1997) challenged the generalization of the minimal jerk model beyond two-joint kinetic systems, and why in their findings the overall trend in RMS-jerk values, when normalized for movement time, were not found to decrease over the course of learning trials? Thanks!
Young, R. P., & Marteniuk, R. G. (1997). Acquisition of a multi-articular kicking task: jerk analysis demonstrates movements do not become smoother with learning. Human Movement Science16(5), 677-701.

04-14-2011, 11:27 PM
Again I don't know this literature well, but I think the minimum jerk theory has been supported pretty consistently for end-point tasks. The results of the Young & Marteniuk study suggest to me that the theory does not necessarily generalize to joint angular kinematics during motor learning. There may be a nonlinear relationship between the jerk of the joints and the jerk of the end-point (the foot, in the case of a kicking task) during the learning process.

Alan Hreljac published a series of papers on smoothness and jerk during whole-body motion that you might be interested in:

Hreljac A (1993). The relationship between smoothness and performance during the practice of a lower limb obstacle avoidance task. Biological Cybernetics 68, 375-379.

Hreljac A and Martin PE (1993). The relationship between smoothness and economy during walking. Biological Cybernetics 69, 213-218.

Hreljac A (2000). Stride smoothness evaluation of runners and other athletes. Gait & Posture 11, 199-206.