Contents:

Project Description

Background

Robotic gait training devices can be helpful in therapy and rehabilitation after neurological injuries such as stroke. However, complex exoskeletons and multi-Degree of Freedon (DoF) robots can prove quite costly. In an effort to reduce the cost barrier for outpatient clinics, Shin et al. (2018) designed a single-DoF, eight-bar linkage in which the length of two bars could be adjusted in order to match a variety of standard gait patterns. Continuing this work, ongoing research within the REWIRE lab is evaluating the performance of further simplified six-bar and four-bar gait training mechanisms for this application (see figure 1). Computational analysis has been performed, but there is no physical prototype of these mechanisms.

Figure 1 Common foot trajectory during gait (left) and series of end effector trajectories from four-bar gait trainer mechanism achieved by varying lengths of links L₄ and L_P.

Project scope

The scope of this project is to build and analyze a four-legged "walking mechanism" using the proportions of the previously described four-bar gait training mechanism for each leg. Household materials were used to build the prototype model. More than four legs would be required to provide redundancy and stability for the mechanism to support itself while walking, but for the scope of this project, the model was limited to four legs. Additionally, the gait trainer would need adjustability in the lengths of L₄ (B-O₄) and L_P (A-P) in order to accommodate a wide range of patient gait patterns according to the patient's natural stride length and stride height (see figure 1). However, for the scope of this project, these lengths were fixed at intermediate lengths within the adjustable range for simplicity.

Design

Link Lengths and Angles

Table 1 shows the link lengths used for each leg of this mechanism. The bold values indicate fixed lengths used in place of the adjustable lengths of L₄ and L_P. Table 2 shows the angles used for the front (left) legs of the mechanism. The back (right) legs are mirrored, such that θ₁ was 137.5 degrees (180 - 42.5 degrees).

Table 1 Link lengths for mechanism legs.

Table 2 Link orientation angles.

Input Crank & Gear Train

Anticipating inefficiencies due to building the model from cardboard and 3D printed parts, the gear train was designed in order to magnify torque passing from the input crank to the two crank shafts. The gear ratio was selected to be 2.25 (N_out/N_in) and the number of teeth on the input crank was selected to be 20 (N_in). Using the property that N_A/N_B = D_A/D_B, as well as the distance between axes, the number of gear teeth and diameter of each gear were calculated as shown in Table 3 below.

Table 3 Gear specifications.

Link 2 - Crank Shaft

The two front (left) legs operate in the forward direction, following a typical human gait trajectory in order to move the robot forward. The back (right) legs are mirrored and follow the mirrored gait trajectory in reverse from typical human gait in order to cooperate, moving the mechanism in the same direction as the front legs. A crank shaft and gear train transmit input rotational motion to the input link (L₂) of each leg. The leg mechanism then transforms simple rotation into the complex motion of the gait trajectory at the “foot” (end effector) of each leg. Each crank shaft has two integrated crank links (L₂) which are offset from each other by 180 degrees. The two crank shafts are offset by 90 degrees with respect to each other. In this way, each leg has its crank link (L₂) in a different orientation at any point in time. This is shown more clearly in video 1 in the following section.

Kinematic Model

Using Matlab scripts built throughout this course and the specifications above, a kinematic model was built within Matlab. Video 1 shows the kinematic model of the mechanism in motion. This model assumes a constant angular velocity of -67 RPM at the input crank. The video shows the mechanism as if it were walking to the negative x-direction (left.) 

Video 1 Kinematic model of walking mechanism.

Solid Modeling

The mechanism was then modeled in SolidWorks in order to verify 3D spatial considerations and prepare the files for fabrication. This stage of modeling was performed assuming that gears, axles, and joints would be 3D printed, and links would be laser cut. Solidworks has a built-in toolbox which was useful for designing the gears of the gear train. The input crank was then modified with a key to fit on a notched shaft. The crank shaft gear was modified to add press fit joints along the axes for the crank shaft, as well as cut windows in the large gears to save time and material while printing. Press fit joints were designed such that the nominal hole diameter was 0.15mm larger than the nominal shaft diameter. This worked well for most joints, however due to inconsistency across parts, some joints fit more loosely than others. The links were designed with the same nominal clearance as the press fit joints with respect to the outside shaft diameter of the 3D printed joint. This allowed for a snug fit of the links on the joint, however the compliance of the cardboard still allowed for relatively smooth rotation about the joints. The bottom tip of the "foot" of the leg's coupler link (link 3) corresponds to the end effector (point P)  which should trace the desired trajectory. Several cardboard spacers were considered to help hold the axial positions of links along long pins or to minimize surface contact between rotating parts. Video 2 below shows an animation of the SolidWorks model in motion.

Video 2 SolidWorks model of walking mechanism.

Prototype

Fabrication

Based on the SolidWorks model, a bill of materials was developed for this project (Table 4). Parts were fabricated from cardboard and wood PLA accordingly as shown in Video 3. Figure 2 shows all of the fabricated components prior to assembly. Labels are provided to help correlate the figure back to the bill of materials in Table 4.

Table 4 Bill of materials for prototype.

Video 3 Sample of part fabrication process.

Figure 2 Fabricated components prior to assembly.

Demo

The assembled prototype is actuated by manually twisting the input crank extension. After assembly, a plot of the Matlab model, including the end effector trajectories, was printed at true scale in order to evaluate the movement of the prototype (figure 3). Due to the compliance of the cardboard, the axles sometimes shift in the transverse direction, allowing an occasional skipping of gear teeth. This happens more often with higher input torques, but applying a gentle twist generates relatively smooth motion. Video 3 shows a demonstration of the prototype on a flat horizontal surface, and shows that the end effector of each leg follows the desired trajectory quite well.

Figure 3 Assembled prototype overlaid on Matlab plot.

Video 4 Prototype demo.

Kinematic Analysis

The four-bar mechanism design which was used for the legs of this prototype was originally motivated for human gait training. In order to use the mechanism for this application, it is important that the end effector not only follows a spacial trajectory typical of human gait, but that the temporal characteristics (velocity and acceleration) also follow human gait patterns. Figure 4 shows the position, velocity, and acceleration data for point P of one leg of the walking mechanism considering a constant input angular velocity of -67 RPM at the input crank. For comparison of the motion patterns over time, figure 4 also shows a sample of ankle trajectory data from previous coursework. The mechanism data is presented at the scale of this prototype, and therefore, the scales do not match for comparison. Additionally, the relative location of the spatial origin is different for the two trajectories. However, the trajectory patterns and shapes can be compared qualitatively regardless of the scale.

Position Analysis

As can be seen in the figure, the shape of the planar trajectory through space closely matches the shape of the trajectory of the experimental data. This was expected as the mechanism was previously designed in order to achieve this objective. The pointed end of the trajectory on the left side of the plots correlates to the heel strike position, and therefore indicates that the direction of forward walking is in the negative x-direction.

Velocity Analysis

As can be seen in the figure, with a constant angular velocity at link 2, the position of point P through time seems to follow a similar general shape to the ankle trajectory. This is due to the fact that both are following a similar spatial path. However, the temporal aspect of the trajectory does not match as well. A clear example is that the magnitude of the negative x-velocity occurring during the swing phase (from maximum to minimum x-position) is significantly higher for the experimental data than for the mechanism. 

Acceleration Analysis

The discrepancy between the mechanism and experimental trajectories is greater for the acceleration plots. The x-acceleration for both graphs follow a pattern of global minimum, followed by local maximum, and then global maximum. But again, the temporal aspects (rate of change) are quite different between the mechanism and the ankle trajectory.

Figure 4 Analysis of trajectory of point P (left) compared to the ankle trajectory from experimental gait data (right).

Discussion

As previously mentioned, in order to achieve a mechanism with sufficient stability to support itself while walking, additional legs would need to be added for redundancy and to avoid the possibility that the mechanism topples as it supports itself on three contact points. A more rigid material than cardboard would be beneficial for the ground link which supports the gear train in order to avoid skipping of gear teeth. The design of the mechanism achieves a good spatial trajectory match for a human gait pattern as per the design of the link lengths. In order to use the four-link mechanism as a gait trainer, however, the linear velocity and acceleration of the end effector should also match that of a human gait cycle. The kinematic analysis here shows that assumption of constant input velocity does not yield accurate velocity or acceleration trajectories. In order for the mechanism to yield a better match to human gait velocity and acceleration trajectories, a more sophisticated controller would need to provide input torque according to a specified curve to match the desired outputs.

Acknowledgements

I would like to acknowledge Jeonghwan Lee for providing background with regards to the gait trainer mechanism, as well as guidance on the link length proportions to achieve a human gait trajectory.

References

Yul Shin, S., Deshpande, A. D., & Sulzer, J. (2018). Design of a Single Degree-of-Freedom, Adaptable Electromechanical Gait Trainer for People With Neurological Injury. Journal of Mechanisms and Robotics, 10(4).

Supplemental Information

Matlab Code