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fast/accurate linear motion on a budget

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I would like to build a juggling machine that can juggle at least 3 balls and mimic the 2d motion of human hands without worrying about the arms.  So I need 2d motion that is very fast (and accurate).  It would be kind of like this machine:

I was thinking that something like the following linear motor configuration would be great (except I would want two 2d bots instead of one 3d bot):

The problem with linear motors is that they are REALLY expensive.  I am willing to spend around $2,000, but with quotes that I have gotten on linear motor prices, my budget would be off by an order of magnitude.  I was wondering if there is some other way that I could do this without spending more than $2,000.

I did some calculations, and it looks like I will need something that will be able to move at 3m/s (or actually 8m/s preferable if I want it to throw at different heights).  The max acceleration would need to be 17m/s^2 (or 60m/s^2 preferable).  Does anyone have any ideas?  Linear actuators are generally slow, and the fast ones seems to be expensive.  Maybe there is some servo that I can use with belt or gears to get the speed/acceleration that I want?  The other piece of information is that the balls would be about 100g, so that would be the load.


Look into buying from surplus outputs and possibly ebay to get stuff at a fraction of their original cost.
You will need to make some design compromises since exactly what you need will not be available.

--- Quote ---Maybe there is some servo that I can use with belt or gears to get the speed/acceleration that I want?
--- End quote ---

would think this type application could be done using pneumatic slides for a fraction
of the costs of servo.


Hmm... I've never heard of pneumatic slides, but it looks like they don't have accurate/consistent velocities, which I think would be a big problem for a juggling machine.  The most important thing for an accurate throw would be to have the correct velocity when throwing the ball.

A brushed DC motor with a good shaft encoder (for velocity) and PWM controller, driving a timing belt, and the pulley traveling along a set of rails with linear bearings, will probably give you the consistency/precision/power you need.


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