Rigid body physics simulation math issue

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To calculate the new positions and rotations of a calf and thigh in a rigid body physics simulation, a joint or pivot point is essential for accurate movement. This joint allows the thigh to rotate and influences the calf's position based on the joint's new location. Visual representations should include a clear pivot point between the two segments to illustrate their connection. Properly implementing this joint mechanism will enhance the simulation's realism. Addressing these mathematical relationships is crucial for effective algorithm training.
NotASmurf
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Hey all, I'm making a physics simulation for training an algorithm of mine, I'm running into issues on the rigid body physics simulation. Let's say I have a leg composed of a calf and a thigh. gravity will be acting on both, and the calf is attached to the thigh, Any suggestions on how I would go about calculating the new thigh and calf positions and rotations? Any help appreciated.

leg.png
 
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I think you need a connecting point like a joint so that as you rotate the thigh rectangle the joint rotates and/or changes position and then you use the joint's new position to calculate the position of the calf object.

So in your fig 1 diagram you need a red dot between to the two rectangles to represent the pivot point of the joint and you need a corresponding red dot in the fig 2 diagram.
 
they are connected, i just did not draw it in, sorry.
 
I do not have a good working knowledge of physics yet. I tried to piece this together but after researching this, I couldn’t figure out the correct laws of physics to combine to develop a formula to answer this question. Ex. 1 - A moving object impacts a static object at a constant velocity. Ex. 2 - A moving object impacts a static object at the same velocity but is accelerating at the moment of impact. Assuming the mass of the objects is the same and the velocity at the moment of impact...

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