Motion Analysis of Interior Gears and Line Spool

Input was the hypoid ring gear, which is the gear that is turned by the human hand, completing one rotation at constant velocity.

This graph shows the position of the pinion gear through one rotation of the hypoid ring gear. The gear ratio is 5.167 so as can be seen on this graph there are about 5.2 rotations of the pinion.

The helical gear which is turned directly by the pinion gear, however this graph shows the position of the helical gear with respect to the input hypoid ring gear. The gear ratio is 4.42 so the helical gear makes 4.42 rotations for every single rotation of the hypoid ring gear.

This graph shows the position of the worm gear through one rotation of the hypoid ring gear. The gear ratio here is 4 as can be seen as the input ring gear rotates once, the worm gear rotates 4 times. 

This graph shows the motion analysis of the middle rod that moves the spool up and down. This rod oscillates so with a constant velocity input from the hypoid ring gear the rod experiences an acceleration and velocity that are not constant and vary with its position.

MATLAB Script:

n1=31;
n2=6;
n3=7;
mv=n1/n2;
mv2=n1/n3;
theta=0;
theta1=0;
theta2=0;
i=1;
w1=1; %angular velocity of hypoid ring gear
w2=mv; %angular velocity of the hypoid pinion gear
w3=mv2; %angular velocity of the helical gear
lwrm=5.5; %length worm gear inches
n4=7.75; %teeth in worm gear
mv3=n1/28;
mv4=n1/n4; %angular velocity of worm gear
radwrm=lwrm*mv3; %length of distance worm gear covers in one rotation of reel handle
div=360/radwrm;
while theta<361
theta1=mv*theta; %angle position of hypoid pinion gear
if theta1>360
theta1=theta1-360;
end
if theta1>360
theta1=theta1-360;
end
if theta1>360
theta1=theta1-360;
end
if theta1>360
theta1=theta1-360;
end
if theta1>360
theta1=theta1-360;
end

theta2=theta*mv2; %angle position of helical gear

if theta2>360
theta2=theta2-360;
end
if theta2>360
theta2=theta2-360;
end
if theta2>360
theta2=theta2-360;
end
if theta2>360
theta2=theta2-360;
end

theta3=mv4*theta;
if theta3>360
theta3=theta3-360;
end
if theta3>360
theta3=theta3-360;
end
if theta3>360
theta3=theta3-360;
end
if theta3>360
theta3=theta3-360;
end
pospool=2.75*cosd(theta/(2*28/31)-180)+2.75;
velospool=(2.75*31/56)*sind(theta*31/56);
accspool=(2.75*31^2/56^2)*cosd(theta*31/56);

x(i)=theta;
y(i)=theta1;
y1(i)=theta2;
y2(i)=theta3;
y3(i)=pospool;
y4(i)=velospool;
y5(i)=accspool;
theta=theta+1;
i=i+1;
end
figure
plot(x,y)
title('One rotation of the reel')
xlabel('Degrees of hypoid ring gear')
ylabel('Degrees of hypoid pinion gear')
figure
plot(x,y1)
title('One rotation of wheel vs. helical gear')
xlabel('Degrees of hypoid ring gear')
ylabel('Degrees of helical gear')
figure
plot(x,y2)
title('One rotation of wheel vs. worm gear')
xlabel('Degrees of hypoid ring gear')
ylabel('Degrees of worm gear')
figure
hold on
plot(x,y3)
plot(x,y4)
plot(x,y5)
legend('position of line spool [in]','velocity of line spool [in/s]','acceleration of line spool [in/s^2]')
title('One rotation of wheel vs. Position of line spool')
xlabel('Degrees of hypoid ring gear')
ylabel('tenths of an inch')
hold off