Robot cinematic model. Which method to get linear and angular speed?

[Patokun]

Hello all! I have a question regarding how to get the linear and angular speed for this robot for example (RRP).

http://img205.imageshack.us/img205/774/rrp.png [Broken]

I am given x and y or the hand, as well as theta (angle)

If I were asked to calculate the linear.

Do I derive x and y to q1, q2 and q3, and fill out the Jacobian matrix to get x' and y'?

Or do I use this formula, where V is speed, R is the rotation matrix, P is the position, etc.. The rotations are on the Z axis.

http://img842.imageshack.us/img842/4438/equationl.png [Broken]

 

[I like Serena]

Welcome to PF, Patokun!

What do you mean by theta?
Is it the angle to the hand in polar coordinates?
If you have x and y, that would imply the angle in polar coordinates.

What do the symbols in your formula represent?


Btw, if you have x and y of the hand, your system in not fully defined yet.
There are many possibilities for q1, q2, q3 to get to a specific x and y.

If however, you have q1, q2, q3, you can set up a formula for x, y, and also for r, theta.
From those you can find linear speed and angular speed.