Aligning 3 point plate - vector cross product useful?

[thomas49th]

Homework Statement

Hello,
I have a plate that needs levelling. I can only twist the back 2 feet threaded feet, while the single front foot is fixed, as in the diagram:

As mentioned above I can only TWIST the back two feet (separately or together) causing the plate to tilt around the fixed front foot.

Given an initial setup where one back foot is higher than another and given that I know the acceleretation due to g in each axis (x,y and z), how do I find the ratio of turn amount of each backfoot to get the system level. That is how many turns on one back foot to the other backfoot is required to bring the system to acceleration:

X axis 0g
Y axis 0g
Z axis 1g

Homework Equations

The Attempt at a Solution

One way of aligning to to align the axis axis first by adjusting the 2 back feet until x-axis is 0, then moving them both the same amount to get y to 0g as well (by moving them by the same amount the acceleration of x-axis is not varied)

I thought perhaps the cross product would help, but it's just a guess

Thanks
Thomas

 

[mighty2000]

Dear Thomas,

Thank you for your question. In order to level the plate, you will need to use a combination of rotational and translational movements. The first step would be to adjust the back feet until the x-axis is at 0g. This can be achieved by using a rotational movement of the back feet, while keeping the front foot fixed.

Once the x-axis is at 0g, you can then use translational movement of both back feet in the same direction to bring the y-axis to 0g. This can be achieved by adjusting the back feet by the same amount, as you mentioned.

To find the ratio of turn amount for each back foot, you can use the fact that the acceleration due to gravity (g) is constant in all axes. This means that the ratio of turn amount for each back foot will be the same for all axes. Therefore, if you know the acceleration due to gravity in the z-axis (1g), you can use this to calculate the turn amount for the back feet in the x and y axes.

I hope this helps. Let me know if you have any further questions.