Pulling on both ends of a stick

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Say two people are grasping a stick in 2-D space and pulling on each end - one person per end of the stick. They can influence the stick's rotation and movement by changing the x and y forces on the ends of the stick - thus, they aren't directly changing the angle the stick is at, although that might be a consequence of their action. Instead, they are each influencing whether their end of the stick is moving up or down, left or right. If I assume that each person s weightless and cannot affect the movement of the stick through their own body weight, how do I determine how the stick moves? Here is the actual problem: I'm starting to experiment with rigid body dynamics, and for my first demo, I want to show a bunch of joints and dynamic bodies all pulling on each other. The dynamic bodies must, for them to do anything, be connected to two joints - the joints don't need to be connected to anything, though. So you could have a free-floating joint, but not a free-floating dynamic (rigid) body. The rigid body pieces keep track of their positions through the joint pieces they are connected to. Obviously, they aren't supposed to change length. However, I'm having trouble thinking of a way to ensure that they pull on the joints, rather than the joints pulling on them, if that makes any sense. Actually, I think what I really need is a good tutorial on implementing rigid body dynamics. If anyone can point me to a good tutorial on this, I would be very greatful. Thanks!

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Check out Chris Hecker's rigid body dynamics articles. They totally rock.
http://www.d6.com/users/checker/dynamics.htm

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Hey, those are good articles! Thanks. Any other suggestions?

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EDIT:

After several hours of thinking, I think I finally know what I need to ask =)
Here is a situation I'm having difficulty modeling:

Say you have two sticks, with one end of each connected to each other in such a manner that the ends must always remain in contact with each other, but so that the sticks can rotate 360 degrees. Say they look like this:

   O  o oO o  o   O

If I apply a force to the right to the "hinge" in the center, how would I determine the force that takes effect on the top and bottom ends of the sticks? I mean, in real life, they would move upwards to allow the center to pass, and then draw towards the center in the X axis, eventually looking like this:

Oo  oo    O  ooOo

How would I determine the force on each end of the sticks? Thanks!

[Edited by - silverphyre673 on November 11, 2005 12:20:06 AM]

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I'd think that if you were in a vacum(ie no air friction) the sticks wouldn't move at all, it would simply travel in it's original shape. the movement would be do to some drag of the fluid the object is moving in, for example water or air. I could be wrong tho, it's an interesting question. I'd think you'd need to model air friction to simulate this.

//edit
the more I think the more I think I'm wrong lol don't wanna confuse what makes it confusing is if you look at it as a single system your exerting force on the center of mass which wouldn't produce anything, but it obviously should

[Edited by - timw on November 11, 2005 5:18:36 AM]

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Any time you have a force acting on an object on a line not through its centre of mass, there will be a torque produced on that object by the force. Torques lead to angular accelerations, which cause rotation, similar to how forces cause linear acceleration and translation.

So, to solve the two hinged sticks and a force problem, you need to work out the torques on the sticks due to the force at the hinge and the resulting angular accelerations of the sticks, and then integrate in time the positions and angles of the sticks (which might in turn change the forces and torques, requiring re-evaluation...)

A reasonable assumption might be that everything is symmetric, so the force F on the hinge is equally distributed on either of the two sticks. Then the torques on the sticks are

T = R x F

where T is torque, F is force and R is the displacement form the centre of mass of the stick to the point of action of the force. R, T and F are all vectors, and "x" denotes the cross product in 3D.

If you're working in 2D, this "simplies" to

T = RF

where R is the perpendicular distance between the point of action and the centre of mass, where the "perpendicular" is relative to the direction the force acts.

Once you have the torque, you can use the relation

T = Ia

where I is the "moment of inertia" and a is the angular acceleration. "moment of inertia" for angular accereration is like the mass for linear acceleration; T = Ia is analagous to F = mA where F is a force, m is a mass and A is linear acceleration.

Note that in general you do still need to consider the linear acceleration of the sticks caused by a non-centred force to fully describe their motion. Also, the hinge also produces some torques and forces of its own, in order to maintain the constraint that the sticks are connected.

You might want to start with a simpler problem of just a single stick and a single force acting on its end, or a stick with equal and opposite forces on either end, or a stick on a fulcrum with forces acting at various places along its length before dealing with the more complicated two stick problem.

[edit: typo, formula fix]

[Edited by - Geoff the Medio on November 11, 2005 4:47:58 PM]

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Geoff, that was a very informative post. Thanks a lot! I think I'll be able to make some progress now. I think I'll get in touch with my old physics teacher from last year and see if he can help me out.

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