(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Determine the position of an object at regular intervals as it accelerates at a constant rate for an unknown length of time, then the acceleration falls to 0 for a given time, then abruptly acceleration goes negative till reaching 0.

the purpose of the calculation is to plot out camera moves for stopmotion animation. the camera begins at a dead stop then is accelerated smoothly to a given speed then decelerated to a stop again. the time over which this takes place is fixed as is the distance the camera travels. the variable here is the number of frames (time intervals of 1/24 second) the accelerations take place over. the are not always the same and one may be zero.

2. Relevant equations

velocity & time:

v=v_{o}+at

displacement & time:

x=x_{o}+v_{o}t+(1/2)at^{2}

velocity & displacement:

v^{2}=v_{o}^{2}+2a[tex]\Delta[/tex]x

3. The attempt at a solution

This is an example problem that the formula I'm trying to figure out would be used to solve.

Ex: The camera move takes place over 15 seconds, or 360 frames (shot at 24 fps) the distance it travels is 29.5 inches (I apologize for the use of imperial units, the dolly rig has a standard threaded leadscrew) The lead in (initial acceleration) takes place over 12 frames (0.5 seconds) the camera moves at a constant speed for a length of time that is dependent upon the 2 periods of acceleration, then the camera has a lead out (deceleration) that takes place over 24 frames (1 second)

I think I need to break the move into 3 parts, Moves 1,2 and 3 or M_{1}, M_{2}and M_{3}

for M_{1}all I know is Time, that portion of the move takes 0.5 seconds.

I don't know distance travelled because it's dependent upon M_{2}and M_{3}and I don't know acceleration because I don't know displacement

for M_{2}I know Time again, 13.5 seconds, Acceleration is zero but displacement is dependent upon M_{1}and M_{3}

for M_{3}the case is identical to M_{1}with Time being 1 second

I know the Total Displacement of the 3 moves but have no idea how to solve for so many unknowns with anything but trial and error. This must be possible as I've seen powerful software programs that operate motion control rigs produce results with only the information I have in my problem. any Help here would be greatly appreciated

Puppetworks

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# Acceleration-Constant speed-Deceleration over fixed distance and time

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