Kinematic Analysis and Calculations

In order to achieve desirable qualities in our mechanism, several adjustments had to be made to the kinematic design. First, we wanted the mechanism to move linearly with the MCP rotation. That is, we wanted the mechanism to move at a uniform speed throughout the mechanism's range of motion, so that the user is not subjected to unexpected accelerations of the fingertip, which could cause discomfort or unease. To do this, we iteratively changed the link lengths of the crank slider and performed analysis on this motion to see if the properties were achieved.

In addition, we also desired that the slider-crank, which was used at a point of attachment for the spring, had a fairly linearly increasing mechanical advantage. This is because the spring, which attaches to the crank output link, will be extending throughout the range of the mechanism, and providing a linearly increasing force. We wanted the resistance element to be as uniform throughout the range of motion as possible, so that the user did not find the beginning portion of the motion to be easy while the end portion of the motion to be difficult. An overview of the mechanism can be found in the next section, for clarity. Again, we iteratively changed the link lengths of the output slider-crank and ran a MATLAB analysis to see whether the mechanical advantage was indeed greater than 1 and increasing over the operating range. Below is the code used to run this analysis.

clear all
%%% input link lengths here %%%
l1 = 63;
l2 = 80;
l4 = 35.81;
w2 = 1; %angular velocity of input, this is a dummy variable and will cancel in M calculation

i = 1;
for theta2 = 37*pi/180:.01:128*pi/180 %for theta in operating range of motion
 %calculate position and velocities using kinematic equations. Calculate
 %mechanical advantage
 theta3(i) = asin((l4-l1*sin(theta2))/l2)+pi/2;
 l3(i) = l1*cos(theta2) + l2*sin(theta3(i));
 w3(i) = -w2*l1*cos(theta2)/(l2*cos(theta3(i)));
 v3(i) = -w2*l1*sin(theta2)-w3(i)*l2*sin(theta3(i));
 M(i) = abs((w2*l1)/v3(i));
 i = i+1;
end
theta2 = 37*pi/180:.01:128*pi/180;
figure(1),
plot(theta2,l3) %plot position vs angle
grid on
title('Slider Position vs. Slider-Crank Angle')
xlabel('Angle (rad)')
ylabel('Position (mm)')

figure(2),
plot(l3,M) %plot advantage vs position
grid on
title('Mechanical Advantage vs. Slider Position')
xlabel('Position (mm)')
ylabel('Mechanical Advantage')

After optimizing the link lengths, the plots of both slider position vs input angle and mechanical advantage vs slider position are shown below.

As shown by the figure on the left, the relationship between the slider position and angle of the finger joint is fairly linear, meaning the fingertip and finger joint will move at a constant rate in relation to each other throughout the range of motion. On the right, the mechanical advantage of the slider crank is shown with respect to slider position. It is clear that the mechanism reaches a toggle position at about 95mm, where the mechanical advantage goes to infinity. However, our operating range exists between 0 to approximately 85mm. In this range, it is shown that the mechanical advantage is increasing at roughly a linear rate, so that for a constant force provided by the fingertip, the slider will be able to extend through its full range of motion, despite the extension of the spring varying the resistance force.