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fast/accurate linear motion on a budget

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MrPrezident:
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:
https://www.youtube.com/watch?v=9asDO_1A27U

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):
https://www.youtube.com/watch?v=9asDO_1A27U

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.

thanks!
-Nathan

waltr:
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.

Tommy:

--- 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.

http://www.ebay.com/itm/Koganei-ORV40X640-Pneumatic-Slit-Rodless-Cylinder-Air-Slide-w-ZE102B-Sensors-ORV-/350837101427?pt=Pneumatic_Hydraulic_Valves_Parts&hash=item51af855373

https://www.google.com/search?q=pneumatic+slide&tbm=isch&tbo=u&source=univ&sa=X&ei=sREIUs-lHrTKyQGQ_ID4Ag&ved=0CEEQsAQ&biw=1366&bih=681#facrc=_&imgdii=_&imgrc=lPZMN8hbFPIFaM%3A%3BXSXuprTBF5kR2M%3Bhttp%253A%252F%252F4tsi.com%252Fwp-content%252Fuploads%252F2012%252F02%252Fbimba-pneumatic-ultran-rodless-slide.jpg%3Bhttp%253A%252F%252Fwww.4tsi.com%252Fmanufacturers%252Fbimba-manufacturing%252F%3B350%3B250

Tommy

MrPrezident:
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.

jwatte:
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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