Relative velocities at ends of rod

[Ketman]

This isn't any kind of homework question. It's a design problem for a mechanical device I'm building.

Two surfaces at right angles to each other, e.g. the corner of a room. If I place a rod across the corner with a wheel on each end and push one end (A) towards the corner (B), the other end (C) will be forced along the other wall at a velocity which I need to be able to calculate. I can see that if the angle between rod and wall is 45 deg. the ratio of the velocities at A and C will be 1:1. But the ratio will be different as the angle changes. I'm guessing that it is simply the ratio of the angles. For example if the angle between rod and wall at A is 60 deg, the corresponding angle at C will be 30 deg, and the velocity ratio will be found as 60/30 or 2:1. Is that right?

 

[SimonRoberts]

I think, just from drawing the 'triangle' that the speed of point C will be equal to the speed of A divided by the tangent of the angle at C.

I'm fascinated as to the nature of this mechanical device though - do tell!

 

[Ketman]

Hmm...multiplied by the tangent would make more sense, surely? Whichever end is closer to B would be going faster. If the angle at C is 30 (i.e, it's further away and going slower), its tan is 1/√3. Dividing by that means multiplying by 1.73, which implies it's going faster. Can't be right.

The device is a crossbow for firing javelin-sized missiles. I'm looking at one found in Hatra in Iraq, which might or might not be Roman, but which has an unusual design. Instead of the wings being pivoted near the centre and pointing backwards in the cocked position, it has each wing pivoted on the outside and pointed inwards. When triggered the wings fly forwards, then outwards.

 

[SimonRoberts]

Sorry yes, multiplied is correct. I kept changing my mind as I tried to picture it, and looks like i settled on the wrong one!