Linear Synergy

Synergies & The Degree of Freedom Problem:

Theoretical & Practical Solutions

by Associate Professor Chris Kirtley MD PhD

The Thalidomide Tragedy

1957 to 1962 in UK, Canada, Germany, Japan - not FDA approved
prevented morning sickness
12,000 babies who survived, with phocomelia (flipper-like arms or legs)
Prosthetic implications

multi-DoF arms
limited number of control sites

Degree of Freedom Problem (Bernstein, 1967)

Shoulder (3 DoF)

Flexion-extension
Abduction-adduction
Internal-external rotation

Elbow (1 DoF)

Flexion-extension

Wrist (3 DoF)

Flexion-extension
Abduction-adduction
Pronation-supination

Prehension (1 DoF: simplest case)

Open-closed

Total = 8 DoF - How to Control?

Eliminate nonessential motions
Couple synergetic motions together

Simpson 5-DoF Upper-limb Prosthesis (Simpson, Edinburgh, Scotland 1963-70)

Hand controlled by Spherical Polar Coordinate reference system:

Elevation
Azimuth
Radial Vector

Clavicular Elevation coupled to Shoulder Abduction
Contralateral Protraction coupled to Wrist Supination
Contralateral Elevation coupled to Prehensor Opening
Clavicular Protraction coupled to

Shoulder Extension
Elbow Flexion
Wrist Supination (cf. biceps brachii) in later MacLaurin prosthesis

Magpie

Oxford Orthopedic Engineering Center (1984)
Single Degree-of-Freedom Coupled Serial Chain (Venkat N. Krovi) $\begin{figure}\begin{center}\begin{tabular}{cc}\hbox{\psfig {figure=AMR/SDC... ...ESIS/CoupledSpatialRRdyad.eps,height=2in}}\end{tabular}\end{center}\end{figure}$
distal joints of a mechanism coupled to the proximal joint

$\begin{figure}\begin{center}\begin{tabular}{c}\hbox{\psfig {figure=AMR/trav... ...psfig {figure=AMR/travis4.ps,width=2.5in}}\end{tabular}\end{center}\end{figure}$

Functional Electrical Stimulation in Paraplegic Locomotion

Flexor Withdrawal Response (Common Peroneal Nerve)

Hip Flexion
Knee Flexion
Ankle Dorsiflexion
Eversion

Extended Physiological Proprioception (Simpson 1973, Childress 1984, Kirtley 1990)

Provides amplification of effort ("power steering")
Force-controlled Position Servo

Walkabout (Kirtley & McKay, 1992)

Linked Hip-Knee-Ankle-Foot Orthosis for Paraplegic Locomotion
Motion constrained to sagittal plane only

Standing posture in children with cerebral palsy (Lowe & Kirtley - External Examiner G Gottlieb)

Support Moment

coefficient of variation (CV) of support moment (14%) lower than the individual CVs of ankle, knee and hip (16, 37 and 33%, respectively)

Four-bar linkage

Swing Phase of Gait

Joint angles correlated in early swing, but not in terminal swing. However thejoint moments are correlated:

Swing Phase Moments in Gait

Method

3D (6-camera) Vicon motion analysis system
BodyBuilder modelling
Swing phase defined when Toe and/or Heel Velocity < Threshold

Normal (natural) Gait

Obstacles

Cerebral Palsy

Covariance between Hip & Knee Moments during Gait

89% between hip and knee and 76% between knee and ankle

Tripping Perturbation (Eng 1997)

hip extensor moment = 1.64 x knee flexor moment

Two-joint MusclesRectus Femoris - Hamstrings

Rectus put under tension (stretched) by hip extension in late stance

Generates flexor extensor moment at knee

Hamstrings put under tension (stretched) by shank inertia during terminal swing

Generates flexor moment at knee

What do you think?

References

Jaks A (1917) Z. Orthop. Chir. 37: 393.

Schede F (1918) Münch. Med. Wochenschr. 23: 616.

Lombard, W.P. (1903). The action of two-joint muscles. Am. Phys. Ed. Rev. 8, 141-145.

Doubler A and D. S. Childress DS, "An analysis of extended physiological proprioception as a prothesis control technique," Journal of Rehabilitation Research and Development, Vol.21, No.1, pp.5-18, 1984.

Eng, JJ, Winter, DA, MacKinnon, CD, and Patla, AE (1992). Interaction of the reactive moments and centre of mass
displacement for postural control during voluntary arm movements. Neuroscience Research Communications, 11, 73-80.

Yang, JF, Winter, DA, and Wells, RP (1990). Postural dynamics in the standing human. Biological Cybernetics, 62, 309-320.

Young, RP, Marteniuk, RG (1995). Changes in inter-joint relationships of muscle moments and powers accompanying the
acquisition of a mult-articular kicking task. J. Biomechanics, 28, 701-713.

White, SC (1986). A deterministic model using EMG and muscle kinematics to predict individual muscle forces during normal
human gait. PhD thesis, University of Waterloo, Waterloo

G. L. Gottlieb, Q. Song, G. L. Almeida, D.-A. Hong, and D. Corcos Directional Control of Planar Human Arm Movement
Journal of Neurophysiology, December 1997/Volume 78, Number 6

Davis, BL and Vaughan, CL Phasic behaviour of EMG signal during gait: use of multivariate statistics. J. Electromyogr Kinesiol 3: 51-60 (1993)

Kirtley C & Andrews BJ (1990), Control of Functional Electrical Stimulation with Extended Physiological Proprioception, Journal of Biomedical Engineering 12(3): 183-8

McIntyre, D.R. & Pfautsch, E.W. (1982). A kinematic analysis of the baseball batting swing involved in opposite-field and same-field hitting. Research Quarterly for Exercise and Sport, 53, 206-213.

Shapiro, D.C., Zernicke, R.F., Gregor, R.J., & Diestel, J.D. (1981). Evidence for generalized motor programs using gait-pattern analysis. Journal of Motor Behavior, 13, 33-47.

Smith, A.W. (1991). The calculation of lower limb support moment during stance in gait using a five-segment model. Journal of Biomechanics, 24(3/4), 243.

Simpson, D.C., and Kenworthy, G (1973), "The Design of a Complet Arm Prosthesis", Biomedical Engineering, vol. 8, #2, pp 56-59.