Support force vectors for a fixed rigid body

[Jellyf15h]

Hello all!

I'm a programmer looking to put together a system modeling the force a character's limbs exert on the environment as that character moves around. Characters can either grasp (with a hand) or press against (with a foot or something) viable contact points in the environment in order to support themselves. Were it not for grasping, I'd be able to do a simple check as to whether the center of gravity lies within the convex hull of the contact points as projected onto the plane perpendicular to the gravity vector. But this case is much more complicated.

I know by now that torque plays an important role in why, exactly, a person's hand and foot exert support forces in diagonal directions as they hold onto a ladder. But with no formal education in statics I'm having some difficulty locating the concepts I need to understand to compute those vectors. Any leads anyone can offer would be immensely helpful.


The specific problem I'm trying to solve (for now) is:

Given the gravity vector g, the set of contact points S, and the mass m and center of mass p of a rigid body (possibly also its rotational moment but I'm not sure that's needed), find the support-force vectors for each contact point.

 

[eljose79]

Hello there! As a scientist with a background in statics and mechanics, I may be able to offer some guidance on this problem. First, let's start with the basics: statics is the branch of mechanics that deals with the equilibrium of objects at rest. This means that we are interested in finding the forces and torques acting on an object that keep it from moving or rotating.

In your case, you are looking to model the forces exerted by a character's limbs on the environment. This involves understanding the concept of force and torque, as well as the principles of equilibrium. Force is a vector quantity that describes the interaction between two objects, and torque is a vector quantity that describes the tendency of a force to rotate an object around a pivot point.

To solve the specific problem you mentioned, you will need to apply the principles of equilibrium. This means that the sum of all forces acting on the object must be equal to zero, and the sum of all torques must also be equal to zero. This will allow you to solve for the support-force vectors for each contact point.

In order to do this, you will need to consider the forces acting on the character's limbs, as well as the forces acting on the object they are grasping or pressing against. This will involve considering the weight of the object, the force exerted by the character's limbs, and any other external forces acting on the object. You may also need to take into account the center of mass and the rotational moment, as you mentioned.

I recommend familiarizing yourself with the concepts of force, torque, and equilibrium, as well as practicing solving problems involving these principles. This will help you understand the calculations you will need to make in order to find the support-force vectors for each contact point.

I hope this helps and I wish you the best of luck in your project! Let me know if you have any other questions or need further clarification.