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Kirstie Yong

Jeonghwan Lee

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Our proposed mechanism has two main parts. First, it includes one link attached to the ground (foot) with a slider-crank that provides resistive feedback at an optimal position to prevent an excessive shank angle

and

where the anterior knee exceeds the big toe (Figure 2). Second, it includes a set of linkages dedicated to provide

visual

proprioceptive feedback to the user when their anterior thigh is parallel to the ground.

, one on the knee and the other on the thigh.

As the person performing the motion progresses through the

exercise

motion, the link attached to the shank (c) will slide up and

eventually

hit the optimal position

,

; any motion forward following

that

will result in the spring deflecting, providing

a

resistance to the knee (

making sure too much

ensuring over flexion does not occur)

. There may be further updates to our design which configure the device in a brace mechanism reducing the need to limit the locomotion of object. Additionally, another key part of the exercise stems from upward and downward motion of the torso once the optimal position is met, therefore we are working to create a mechanism which allows the user to be notified on the thigh when they have reached the bottom of their motion

.

The kinematic challenges involved with our mechanism include:

1) Determining

 

where the spring must be positioned to optimally provide

the

resistive force against further motion such that the knee does not move past the user's big toe.

2) Determining the optimal linkage lengths for

the For the slider crank mechanism attached to the shank

the thigh proprioceptive feedback.


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Figure 2: Kinematic analysis and design diagram overview


To address the first kinematic challenge, the slider position

p

can be calculated as a function of the ankle joint angle

θ. First, the ankle joint angle of the optimal posture θopt will be acquired

θ2 (Figure 3). The optimal value of θ2 can be determined by geometric positional analysis based on the user’s anthropometric data when the knee and longest toe are in line

(Figure 4 (b)). Since the position of the slider p must be calculated as a function of the ankle joint angle θ, the slider position of the optimal posture popt will be calculated from the determined ankle joint angle θopt. In the same manner,  pmin and  pmax will determine what to set as the travel distance (dtravel ), the safe range of motion to minimize risk of injury. However,  popt and dtravel are different between individuals since θopt varies depending on the user’s body segment length. Since differences in  popt and dtravel vary between individuals, device calibration is necessary before using such as changing spring position and the range of motion. Changing spring position is not just the stretch distance of the spring. Changing spring position means adjusting the threshold and changing the range of motion adjusting physical restriction of back and forth motion at knee motion. The ideal design would account for the spring length to not change. To avoid potential additional adjustments for different sized bodies,  popt and dtravel  will require additional positional analysis based off different shank length to foot ratios to investigate whether the travel distance changes drastically between different sized people. If the optimal position and travel distance varies a negligible amount, then a fixed universal spring placement and range of motion will be calculated to give any user some flexibility in motion. If the optimal angle varies a non-negligible amount, then more detailed positional analysis is required to calibrate device.The second kinematic problem involves the slider moving above the thigh link. We must calculate the angle gamma such that a button (blue dot) is clicked when the thigh is parallel to the ground. This requires

. Then, using the vector loop method, we can then solve for θ4, the angle of the linkage arm attached to the slider, and b, the distance the slider must travel. These equations allow us to calculate how long our shank links need to be and where the spring should be placed to hinder further motion. Using these equations, we tested different linkage lengths to see what provided the most optimal position by plotting them in MATLAB as seen in Figures 8 and 9. The plots provided us the visuals we needed to determine what would stop the knee (point A) from moving too far forward. The ankle joint angle and the slider-crank angle are plotted in Figure 7 (a) to show how much the slider-crank link must move in order to accommodate the inputted knee angle. And the horizontal displacement of knee and displacement of slider from ankle are plotted in Figure 7 (b) to show how the desired spring placement is determined. 

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Figure 3: Positional analysis using the vector loop equation to solve for θ4 and b.


Addressing the second kinematic problem, we performed another vector loop equation analysis on a local x2y2 frame between links f, g, and h. This required a more difficult kinematic analysis because the thigh

mechanism is

feedback linkages are coupled to the shank link

;

, and it

will involve

involved determining relative positions between the thigh and shank linkages

.

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Figure 1: Kinematic analysis overview

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Figure 2

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Figure 3

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Figure 4

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Figure 5

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Figure 6 

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Figure 7

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Figure 8

. From this process, we could derive equations (2) and (3) as seen in Figure 4 which have four unknowns: f, g, h, and θ5.

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Figure 4: Positional analysis using the vector loop equation to set up equations (2) and (3) for solving optimal lenghts of f and g.


In order to calculate the lengths of f and g, we had to first determine h and θ5. We used two known conditions, an optimal and neutral position, which provided us the parameters to determine the value of θ5 and h, reducing our unknowns to only f and g. Figure 5 below details each condition and shows how we solved for θ5 starting from knowing θ2 in the optimal position and how we solved for h in the neutral position. Figure 6 below provides the final two equations (5) and (6) which enabled us to define all geometry for our mechanism.

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Figure 5: Two known conditions: optimal and neutral, which provide the necessary parameters to solve for link lengths of f and g.


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Figure 6: Equations (5) and (6) used to calculate link lengths of f and g.


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(a)

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(b)

Figure 7: (a) Plot of relationship between input (knee) angle and output (slider-crank) angle. (b) Plot of relationship between horizontal displacement of input (knee) and distance from ankle to slider.


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Figure 8: MATLAB plot of entire mechanism in its neutral position.

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Figure 9: MATLAB plot of entire mechanism in its final optimal position, catered to one user's anatomy.