dav_i
Mar30-11, 01:59 PM
1. The problem statement, all variables and given/known data
Hi there,
In my experiment I have a disc which needs to be pitched and rolled about it's centre. The disk is mounted by three verticle "pistons" one every 120degrees. I need to convert a tilt in the x-direction \theta_x and a tilt in the y-direction \theta_y to how much each piston should be raised and lowered by. An additional constraint is that the centre of the disc must stay at the same height.
I've been bashing my head against a wall with this for what seems like forever and any help will be appreciated...
2. Relevant equations
We name the positioners A, B and C at height z_{a,b,c} and the angle from origin O to A is \alpha O to B as \beta and O to C \gamma.
The direction O to A is at an angle of \Omega to the x-axis.
The length of O to A is r.
3. The attempt at a solution
I figured out that
\alpha = \theta_x\cos\Omega + \frac{\sqrt{3}}{3}\sin\Omega+ \theta_y\frac{\sqrt{3}}{3}\cos\Omega-\theta_y\sin\Omega
and
\beta = \theta_x 2 \frac{\sqrt{3}}{3} \sin \Omega + \theta_y 2 \frac{\sqrt{3}}{3} \cos\Omega
From here I get stuck: I've tried many things but I know they're wrong (as in my experiment it doesn't work properly!)
Any help please, thanks in advance
Hi there,
In my experiment I have a disc which needs to be pitched and rolled about it's centre. The disk is mounted by three verticle "pistons" one every 120degrees. I need to convert a tilt in the x-direction \theta_x and a tilt in the y-direction \theta_y to how much each piston should be raised and lowered by. An additional constraint is that the centre of the disc must stay at the same height.
I've been bashing my head against a wall with this for what seems like forever and any help will be appreciated...
2. Relevant equations
We name the positioners A, B and C at height z_{a,b,c} and the angle from origin O to A is \alpha O to B as \beta and O to C \gamma.
The direction O to A is at an angle of \Omega to the x-axis.
The length of O to A is r.
3. The attempt at a solution
I figured out that
\alpha = \theta_x\cos\Omega + \frac{\sqrt{3}}{3}\sin\Omega+ \theta_y\frac{\sqrt{3}}{3}\cos\Omega-\theta_y\sin\Omega
and
\beta = \theta_x 2 \frac{\sqrt{3}}{3} \sin \Omega + \theta_y 2 \frac{\sqrt{3}}{3} \cos\Omega
From here I get stuck: I've tried many things but I know they're wrong (as in my experiment it doesn't work properly!)
Any help please, thanks in advance