New design aspects of a locomotory rehabilitation mechatronic system.

Seiciu, Petre Lucian ; Laurian, Tiberiu ; Filipoiu, Ioan Dan 等

1. INTRODUCTION

Walking is one of the most important features of humans. Walking failure leads to serious problems in fulfilling the most common daily activities such as stair climbing, sidewalk walking and street crossing leading in time to total loss of the limb control. Therefore the scientific study of the human movement is mandatory both for its theoretical understanding and for medical purposes. The mechatronic technology and virtual reality in rehabilitation proved to be promising research directions. The modern rehabilitation methods were used only in the last period at a small level, due to a lack of equipments. The use of the gait trainers, as a new method appeared like an alternative to the classical rehabilitation. The results are similar to the classical methods. A consistent difference appeared with the use of the mechatronic gait simulation systems. In this moment there are only a few systems operating (in Germany, Switzerland and USA).

The designing and assembling of the state-of-art mechatronic system (MS) presented in this paper lead the authors to the conclusion that a more thorough scientific study of the walking is needed in order to improve MS functioning (Filipoiu et al., 2007). The main goal is a new design of the foot driving system (FDS), since this is the most complex feature of the MS, mainly due to the foot complex movement.

2. WALKING--PEDALING ANALOGY

The most difficult task in the design of the FDS (figure 1) is to replicate human walking as close to reality as possible.

That is why walking is studied intensely by scientists world-wide.

There are several theories that study walking (six determinants of gait, inverted pendulum, dynamic walking etc.) but none of them is fully applicable for design purposes.

Figure 2 presents a comparison of kinetic parameters from a dynamical simulation with the experiments (Zajac et al., 2003). The black lines (kinetic trajectories) are plotted from the simulation and the grey lines (average kinetic trajectories) are plotted from experimental subjects. VGF and HGF are the vertical and horizontal ground reaction forces from subject measurements. AM and AP are the ankle moment and power computed from inverse dynamics by using subjects' measurements of ground reaction forces and kinematics.

The forces are normalized by body weight; moment and power by body mass.

[FIGURE 1 OMITTED]

[FIGURE 2 OMITTED]

In pedalling, muscles have to produce energy over the crank cycle and deliver the energy to the crank to overcome crank resistance and inertia. Muscles deliver power to the crank by developing a tangential crank force. Power delivered to the crank is calculated by (Zajak et al., 2002, 2003).

P = [omega] x T = [omega] x r x [F.sub.t] = [omega] x r x F x cos [alpha] (1)

where co is the crank angular velocity, T is the crank torque, r is the crank arm length, [F.sub.t] is the tangential crank force, F is the normal force on the pedal and [alpha] is the instant angle. All the terms are determined or measurable. The energy delivered to the crank over the crank cycle (0 - 360[degrees], figure 3), which is the external work done on the environment in a cycle, can be calculated by integrating crank power over the cycle.

A comparison between simulated and experimental hip, knee and ankle powers, during the crank cycle, is presented in figure 4 (Zajak et al., 2002). Experimental data are plotted as grey lines and simulation data as solid lines. Propulsive energy to the crank occurs during leg extension (the area above 0 line, during 0 / 180[degrees] crank angle) is positive.

If we consider the ankle diagrams in figure 3 and 4 we can observe easily that the 2 lines are almost similar.

[FIGURE 3 OMITTED]

[FIGURE 4 OMITTED]

This can lead to the conclusion that the study of pedalling, under some conditions is similar to the study of walking.

3. MECHANICAL WALKING ENERGY ASPECTS

Human walking is theoretically explained by two prevailing, but contradictory theories. The first theory called "The Six Determinants of Gait" (SDG) aims to minimize the energetic cost of locomotion by reducing the vertical displacement of the body centre of mass (COM). The second theory called "The Inverted Pendulum Analogy" (IPA) suggests that walking is a movement combination of two pendulums: the inverted pendulum for the stance leg and a direct pendulum for the swing leg. Walking efficiency is considered for these two theories in order to design properly the mechatronic system. According to the SDG theory, the cost of transport depends on the relative proportions of single and double support. The most economical flat COM trajectory is achieved with single support dominating the step and with an instantaneous double support phase. The dimensionless work rate is (Kuo et al., 2007)

WR = [s.sup.2] x f/4 x [square root of 4 - [s.sup.2]] (2)

The IPA theory states that the dimensionless positive work rate is (Kuo et al., 2007)

WR = 1/8 x [f.sup.2] x [s.sup.2] (3)

where s is the step length and f is step frequency, normalized by the natural frequency of the leg.

The theoretical lower limit for the cost of transport (Collins et al., 2005) in walking models is [c.sub.mt] = 0. This can be achieved by swaying the upper body with springs in such a manner as to totally eliminate the collision losses. Without swaying the upper body, a rough lower bound on energetic cost can be estimated from the point-mass small-angle model

[c.sub.et] [greater than or equal to] [c.sub.mt] [greater than or equal to] J [(s - [s.sub.f]).sup.2] x [v.sup.2]/2 x g x d x [l.sup.2] [approximately equal to] 0.0003 (4)

where J is the collision reduction factor, which is 1/4 for pushoff before heel-strike, s [approximately equal to] 0.4 m is the step length , [s.sub.f] [approximately equal to] 0.2 m is the foot length, l [approximately equal to] 0.8 m is the leg length, v = 0.4 m/s is the average velocity, and g [approximately equal to] 10 m/s2 is the gravity constant.

Another dynamical model (Kuo et al., 2002) find out that [c.sub.et] = 0.003. Other values of [c.sub.et] for real models (Collins et al., 2005) are presented in table 1.

4. CONCLUSIONS

The most significant conclusion is that the analogy between walking and seated pedalling is very useful for FDS design, due to the simplicity of the pedalling model.

A total new conclusion is that the SDG theory applies best for the new MS design, since it uses a flat COM trajectory.

The cost of transport can be estimated easily, but the results vary largely from one application to another. We aim to reach low cost of transport values with the above conclusions applied in the newly designed MS.

All these conclusions will lead to a newly designed MS which will simulate walking closer to reality and, hence, a better and more efficient recovery of the persons with locomotory disabilities.

5. REFERENCES

Collins, S.; Ruina, A.; Tedrake, R. & Wisse M. (2005). Efficient Bipedal Based on Passive-Dynamic Walkers, Science Magazine, Vol. 307, no. 5712, February 2005 p. 1082-1805, ISSN: 0036-8075

Filipoiu, I. D.; Seiciu P. L.; Laurian, T. & Carutasu, N. (2007). Mechatronic System for Neuro-Motor Disabled Persons: Computer Simulation, Ann. DAAM proc. Int. DAAM Symposium, Katalinic, B. (Ed.), pp. 281-282, ISBN 3901509-58-5, Zadar, Croatia, 24-27th. October 2007, DAAAM International Vienna, Vienna

Filipoiu, I. D.; Seiciu P. L.; Laurian, T. & Carutasu, N. (2007). SIMESIM--The Mechatronic System For Neuro-Motor Disabled Persons, In.: DAAM International Scientific Book 2007, Katalinic, B. (Ed.), pp. 387-398, DAAAM International Publishing, ISBN: 3-901509-60-7, Vienna

Kuo, A. D. (2002). Energetics Of Actively Powered Locomotion Using the Simplest Walking Model, Journal Of Biomechanical Engineering, ASME, Vol. 124, Issue 1, February 2002, pp. 113-120, ISSN: 0148-0731

Zajak, F. E.; Neptune, R. R. & Kautz, S. A. (2002). Biomechanics and Muscle Coordination of Human Walking. Part I. Gait and Posture, Vol.16, Issue 3, December 2002, pp. 215-232, Elsevier, ISSN: 0966-6362

Zajak, F. E.; Neptune, R. R. & Kautz, S. A. (2003). Biomechanics and Muscle Coordination of Human Walking. Part II. Gait and Posture, Vol.17, Issue 1, February 2003, pp. 1-17, Elsevier, ISSN: 0966-6362

Table 1. Estimated cost of transportation for various robots.

Cornel biped Deft robot MIT learning
 biped

 0.2 5.3 10.5