Given a weight and the angle of the legs, how do I calculate how much force each leg of a chair supports?I'm kinda-sorta sure of how to do this problem in 2D, but I have no idea how to do it in 3D.
I would need to see the 3D picture to be sure, but..... Assuming the weight is symmetrical about an axis through the chair: Solve it as a 2D problem on a plane passed through the axis of symmetry. Then distribute the weight to the legs on each side of the plane. Example: You are sitting in the chair. You mass is 100 kg (weight: 980 N). The chair has a weight of 20 N. Total Load is 1000 N. The plane splits your body in half (the left half of your body is on the left half of the chair). You solve the moments about the center of gravity for the rear legs and find the rear legs support 750 N ==== Each rear leg supports 750/2 = 375 N This means each front leg supports (1000 - 750)/2 = 125 N
find the force for all four legs and divide it by 4
the amoutn of force divided by 4, since there is 4 legs in a chair
Assuming that each leg is identical and positioned at equal distances to each other, they should each support an equal fraction of the total weight, unless the weight isn't being put on the chair equally. e.g. if a four-legged chair, with legs peripendicular to the floor, has to support 100lb, each leg should support 25lb each. If the legs are at an angle, just use the leg as the hypotenuse of a right trangle, the 25lb as one side of the angle, and use trigonometry to find the force (length) of the hypotenuse.
There are several factors to consider. The weight of the chair + the object on the chair divided by the number of legs the chair has. The angle of legs will not matter. What matters is the placement of the object on the chair. Unless specified, You assume the object on the chair is center. But if calculating for a person setting on the chair you may have variables on placement of weight ratios front to rear. This is usually compensated for(on average) by the rear legs being angled back to push the center of mass forward seeking a balance so all of the legs support the same (approximate) weight. I hope you found this helpful. P.S. If you have access to several matching scales you can place a chair with each leg on different scales. Have a person sit in the chair and observe each scale. Next use something else like a stack of books and place them on different areas of the chair to see what happens.
