Simulation .…

3.2.1 Linearization

Based on the result of gait analysis, we arbitrarily set the peak of angular acceleration to be at 3~18% of gait cycle after the heel strike (which is at gait cycle of 0% & 50% for the other leg). The peak of angular acceleration occurs at -10°~10° of hip-ext/flexion angle. By substituting the hip angle ‘θhip’ into our model mentioned, as shown in Figure 3-3 , we obtain the length of cable from knee to the exit of sheath on the waist, which show highly linear relation with ‘θhip’ within the range. As shown in Figure 3-6, we find that the slope of cable length ‘lcable’ over ‘θhip’ is insensitive to change of ‘l1’ within 35 to 45 cm, which covers the average length of the distance between hip pivot and knee pivot for male with body height from about 150 cm to 180 cm if we assume this length is linearly proportional to body height. Also, we find that the slope is insensitive to variation of ‘b’ from 5 to 15 cm. Though there is a 0.017 cm per degree change in slope for every 1cm change in ‘a’ from 5 to 15 cm, yet it is small in comparison the scale. Therefore, we assume the relation between cable and ‘θhip’ as:

0.1732 1

cable hip

l   c (37)

where ‘lcable’ in cm, ‘θhip’ in degree, and ‘c1’ is constant that varies from each wearer.

By differentiating equation (37) with time, the relation of change rate of length, which equals to linear velocity, and the angular velocity is obtained. Then, we substitute the peak angular velocity from our curve-fitting data and acquire the maximum linear speed during a gait cycle is 63.31 cm/s.

Figure 3-6 plot of ‘lcable’ within the range of ‘θhip’ from -10° to 10° with

(a) ‘l1’ varies from 35~45 cm. (b) ‘a’ varies from 5~15 cm. (c) ‘b’ varies from 5~15cm.

We replot the curve of ‘θhip’ over gait cycle with ‘θhip’ replaced with ‘lcable-θ

hip’ relation, as shown in Figure 3-7. We arbitrarily define ‘c1’ to be zero and set the origin to be at ‘θhip’ = 0. We replicate a mirrored version with 50% phase lag in gait cycle as the pattern of the other leg under the same gait cycle. These two curves, representing positions of each leg in the view of our actuation device, are denoted as

‘Xr’ for right leg and ‘Xl’ for left leg, respectively. We then form an approximated position trail for the slider, denoted as ‘Xs’. The slider will first be pulled by the leg swinging backward from the origin passively, then actuate to provide assistive force to drive the leg swing forward for a distance, and finally return to the origin to wait for next actuation cycle. In this trail estimation, we set the point of return to be at ‘Xs = ± 2’, which locate in about 18% phase in gait cycle after heel strikes, located in gait cycle of 0% and 50%.

Figure 3-7 the estimated position trajectory of the right leg (Xr), left leg (Xl), and slider (Xs) during ground level walking. Here flexion positions of right leg are positive, which corresponds to the right leg angled towards the front of the body or the slider moved towards the left leg side.

As a simplified version of assistance, as shown in Figure 3-8, we replace the return stage by a brake. The slider will be pulled and then provide assistance until returning to Xs =0. As the actuation is over, the slider brakes, remaining its current position, and wait for next actuation cycle. In this trail estimation, we assume that it takes 1cm length for slider to brake.

Figure 3-8 the estimated position trajectory of simplified version

3.2.2 Simulation result of device actuation

Since the true gait pattern of human is complicate and hard to predict, we first evaluate the effect of our device by seeing how our device affects the torque and power needed to maintain the same gait pattern. Figure 3-9(a) shows the moment ‘Mhip’ required for the original gait pattern, in which the moment that drives thigh swinging forward is positive. By multiplying the angular velocity, shown in Figure 3-9(b), we can calculate the power requirement in each phase of gait cycle, and the amount of power that needs to be input or dissipated to maintain the same kinematical properties of gait, as shown in Figure 3-9(c). Because the gait cycle is in linear relationship with time, the area formed by power curve and the horizontal line at 0 represents the energy needed. A positive area means the insufficient amount of energy, which deaccelerates the system if there is no external energy input. A negative area means the surplus amount of energy, which accelerates the system when there is no energy dissipates from the system. By integrating the power with gait cycle, the amount of insufficient energy is 0.3440 J/kg larger than that of surplus energy in a gait cycle as a result, which means that people need to do efforts every step to remain the same gait.

Figure 3-9 Simulation result (a) hip moment required (b) angular speed of hip joint (c) power required to maintain original gait pattern without assistive force from device.

We assume that our device will provide a constant-force assistance of 100 N with direction varies with angle of hip joint, with relation mentioned in equation (33), during gait cycle form 50% to 65%, in which phase leg swings forward. Since there is no gait data for assisted walk, we assume that the gait pattern will remain the same. As shown in Figure 3-10(a), there is a downward shift in moment requirement from 50% to 65%

of gait cycle, and the amount of insufficient energy drops to 0.2873 J/kg per cycle, which means 3.589 J of energy requirement is preserved with the application of 100 N assistive force during the analysis.

Since human beings, unlike robot, would normally rather take advantage of assistive force than resist it to maintain the original gait pattern after training, the gait pattern tends to change, or at least to accelerate, if assistive force is applied. To estimate how gait will change with assistive force applied, we use ADAMS to perform Figure 3-10 Simulation result (a) hip moment required (b) angular speed of hip joint (c) power required to maintain original gait pattern with assistive force, where dotted lines are the original moment and power pattern as shown in Figure 3-9.

simulation of gait cycle from 50% to 68%, assuming that every joint force and moment will follow origin moment pattern with ‘θhip’, and constant assistive force of 100 N is applied. Since we design our device to track the position of the slider, the simulation starts with the gait pattern in 50% gait as initial conditions, and will end when ‘Xs’ reaches 2, which means ‘θhip’ reaches 10.56° according to equation (37). Also, we assume that wearer will remain the same moment and force relation at knee joint, ankle joint, and the same ground reaction force relation with ‘θhip’ since the assistive force is actually an internal force and should only cause redistribution of load between thigh and upper body if we view the whole wearer as a system. However, due to the absence of muscles, which provide sufficient constrain for leg, the linkage leg, especially the linkage calf, swung like a pendulum and the simulated gait is quite different from the original gait pattern, even when the assistive force was removed.

Table 3-2 Initial angle & velocity for simulation

Hip Knee Ankle

θ1 -98.5107° θ2 -112.2744° θ3 -61.2715°

ω1 -0.2892 rad/s ω2 -3.8178 rad/s ω3 -8.7701 rad/s

Figure 3-11 Moment, ground reaction force, and joint force pattern for simulation