# Tricycle physics

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EDIT: I found the resources I need after posting this on: http://planning.cs.uiuc.edu/node658.html

Hello all,

I am trying to workout how a pallet jack (esentially a tricycle) would travel. I'm looking at top-down 2D here.

My current setup is that I have a handle fixed to a point on the jack body, with an angle independent of the jacks body. The jack body then has an angle, and as the jack moves forward (as in you pull the jack along), it's angle would converge by some constant on the handle angle. When pushing the pallet jack it would instead diverge by some constant until the handle hits some maximum angle and then the jack would spin on the spot.

This works OK, but it there are some mistakes. When the handle is 90 degrees from the jack body, it should spin with the center of rotation being exactly between the two fork wheels. Using this method I couldn't figure out how to rotate about the correct spot. I thought about just having edge cases be handled different, but I was hoping someone knew of a better all encompassing solution. Either using friction/drag and other physics concepts, or just using geometry.

I tried using geometry and trigonometry to calculate some circle that the jack should be travelling along but I haven't had any luck.

Am I over complicating this? I'm not search how to search for "physics of pulling an object behind you with drag", so I haven't been able to find any resources.

EDIT: Finally found something on google (now realizing that the same problem applies to 4 wheeled vehicles), I reached this same sort of solution, but I am stuck on how the jack moves along the circle:

Edited by Aksel Huff

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When you apply a force to the handle, assuming the rear wheel is always aligned to its direction, you can consider the longitudinal component and the lateral component separately. The lateral component adds a torque which causes a rotation around the mid point between the forward wheels. The longitudinal component makes the jack advance or backup.

F_long = F * cos(alpha)

F_lat = F * sin(alpha)

where alpha is the angle you are turning the handle.

At 90 degrees, there is no longitudinal component as cos(alpha) = 0, but sin(alpha) = 1 so it is pure torque and the jack should indeed spin in place.

Assuming the handle is applied to the center of the rear wheel and the distance between the axle of the rear wheel and the midpoint between the front wheels is L, then the rotational torque is:

T = F * sin(alpha) * L

With the forces and torque known, assuming you know mass and moment of inertia around the Z (pointing up) axis, you can calculate the accelerations, then integrate to determine the velocities and integrate once more to determine position and angle of your jack.

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Thank you very much! Wasnt sure if my question made enough sense to get and answer, but you gave me exactly what I was looking for!

I dont fully understand a few things here, but it's a great starting point for me to go learn some more stuff. I'll report back if I have any more questions.

Thanks again!

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4 hours ago, vr_marco said:

With the forces and torque known, assuming you know mass and moment of inertia around the Z (pointing up) axis, you can calculate the accelerations, then integrate to determine the velocities and integrate once more to determine position and angle of your jack.

Are you able to go a little more in depth with this?

Calculating the forces and the torque is easy enough, and I found a formula for moment of inertia so I have that. (I assume the Z axis is on the midpoint between the fork wheels?), but then I am completely lost. I found a formula for angular velocity using torque and inertia, but I don't know what to do with it.

I don't know what integration is, do you know of a good resource, or what I need to learn first? I've tried watching a few videos on youtube about it, but I don't understand at all what they are talking about.

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So you know that

Torque = Inertia * Angular Acceleration

and therefore

Angular Acceleration = Torque / Inertia

Now, since angular acceleration is the time derivative of angular speed, to get angular speed from angular acceleration you have to do the inverse operation of a derivative, which happens to be an integration. The easiest way to do it is to use Euler’s integration:

Angular Speed [current frame] = Angular Speed [previous frame] + Angular Acceleration * Delta Time between frames

Once you have the Angular Speed, you can apply once more Euler’s integration to get the rotation angle.

In this way you have linked the input Torque to the rotation (angle) of your jack.

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