# What would you call this mechanism and how can I calculate the forces involved

So I have an assembly with two pins sliding in two groves. First I would like to know if there's a name for this so I can do some more research. Second, if the assembly is standing up so that the top pin travels vertically and the bottom horizontally, how can calculate the force applied to each pin. So say I hung a 1kg mass on the top pin, how much force will be transferred horizontally?

• I don't know the name of this assembly, but I think you can calculate the forces using simple mechanics. Also, you will need to know the friction coefficient and determine whether it is permitted to slide (horizontally) or not.
– r13
Jul 8 at 1:40
• This looks to be the same or similar math as a truss. It's just a free-body diagram question really. Jul 8 at 1:49
• which parts are movable in relation to other parts? Jul 8 at 6:25
• friction is an important part of reality. decide wisely how you account for it.
– Abel
Jul 8 at 7:44

This is a type of ellipsograph or Trammel of Archimededs.

It's a mechanism that is widely documented in textbooks for both the kinematics and the dynamics.

Regarding the second part of your question, it really depends on two things:

• the position of the rod (angle)
• the velocity at the point of calculation.

In the simple case of velocity equal to zero, then if the angle with the horizontal is $$\theta$$, if you do the equilibrium of forces on X, Y and the moments, you will find that:

$$F_{hor} = \frac{P}{tan\theta}$$

where:

• $$F_{hor}$$ the horizontal force
• $$P$$ is the load on the top pin
• $$\theta$$ is the angle of the connecting rod with the horizontal axis.

Keep in mind that in the dynamic case, ie.if the rod is moving (has an initial velocity) then the forces will be different. That can also be calculated in a variety of ways.

UPDATE: I see a lot of people are commenting about friction. If that's the case, then the velocity and the application of the load will determine the direction of the friction force. However, again, the calculation is very simple in the static case, with branches depending on the position and the direction of the load.