This past season my team had a shooter arm rotate about a shaft powered by a chain and sprocket. The first step in a successful design is selecting the correct motor and reduction. The RS775 is a great motor but it doesn't do the best when stalled as its fan needs to be spinning for it to stay cool. You can check out the amazing resources at Vex Pro (
http://motors.vex.com/) to see the very elaborate motor testing they have performed. Towards the bottom of this page (
http://motors.vex.com/bb-775) you can see the locked rotor stall test. The graph shows that over just 20-30 seconds a stalled 775 will burn out and provide no torque. Taking that into consideration, I would recommend a bag motor (
http://www.vexrobotics.com/217-3351.html) Although it has a lot less power, it is okay with being stalled for a little longer (
http://motors.vex.com/bag-motor)
That being said, there are some amazing resources out there to help you design a chain driven arm. The first and a tool I use very often is JVN's design calculator. Don't forget you can get a reduction in your gearbox and in the sprocket.
https://www.chiefdelphi.com/media/papers/3188
Using this very simple spreadsheet you can mess around with different motors and reductions until you get the speed and power draw you are looking for. I suggest you use the "Rotary Mechanism" tab for your current project.
As for what gearbox to use, there are quite a few choices but my team and many others have successfully used vex pro VersaPlanetary gearboxes (
http://www.vexrobotics.com/vexpro/mo...planetary.html) they are very flexible and can be used in many different gear ratios.
Finally, once you have your reduction picked out you will need to calculate the spacing between the two sprockets. This site (
http://www.botlanta.org/converters/d.../sprocket.html) has worked well for us. I would use your mill with a DRO to machine a perfect center to center between the sprockets. If you choose not to do this, you can always use a chain tensioner of some sorts, there are many different designs out there.
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2016:
Deans List Semi-Finalist/MAR Mount Olive District Engineering Inspiration Award/Buckeye Regional Second Alliance Captain/MAR Montgomery District Event Imagery Award/MAR Championship Gracious Professionalism Award
2015:
MAR Mount Olive District Chairman's Award/MAR North Brunswick District Winners/MAR Championship Finalists
2014:
MAR Clifton District Chairman's Award/MAR Championship Regional Chairman's Award