Does adding omni wheels to the front of your robot move the turning center backwards or forwards?
Backwards. Thinking through the math has me stumped for a while (Finals are really draining my brain right now) but the center of rotation will in general be closer towards the traction wheels.
Hi first_newbie, I notice you are asking a lot of good “beginner” questions. That’s cool - I’m still kind of a beginner too and I don’t know the answer to all your questions (including this one).
However, this forum is a historical archive of years of experience from thousands of students and mentors - and a great way to learn is to just read, read, read. There are some great forum search tools if you want to learn more about specific topics!
You are correct, it is backwards. It’s because there are very little to no lateral scrub forces by the omnis.
The primary determining factor of the center of rotation is the center of gravity. Both traction and omni wheels tend to move the center of rotation towards their axles due to frictional forces as the wheels do not move along the floor at the same speed as they rotate. Having more friction, traction wheels do this better than omnis.
You’ll now have to explain from that why a robot with traction wheels only at one end and omnis everywhere else (at the other end only, or at the other end and in the middle) rotates around near the traction-wheel end, regardless of center of gravity location.
I’ve seen that phenomenon way too often. A good robot designer can put the center of rotation right where he/she wants it, for a variety of reasons (like aiming easily, or keeping a stack from moving as violently). One old trick is to put the omnis on opposite corners of the robot (494, 2006) to keep the center of rotation in the middle of the robot.
The short version is that the center of rotation will move towards the traction wheels and away from the omni wheels. The reason would be that the force resisting turning is now much smaller at that end (traction wheels have massive resistance to going sideways, particularly compared to omnis), so it will turn very very easily. This will put the majority of the force acting around a point that is in the middle of the forces generated by the traction wheels. Not all of it by any means, but enough of it.
This is why we do the math.
The math:
http://www.chiefdelphi.com/media/papers/1443
This section of the VEX Robotics curriculum may also help explain some of the concepts behind your question:
http://curriculum.vexrobotics.com/curriculum/drivetrain-design/drivetrain-terminology-and-turning
I can’t believe that paper is over 12 years old!
Wow I am old. How did that happen?
I didn’t notice anything in there about omni wheels (or wheels with different scrub forces under the same conditions). μ[sub]y[/sub] is the same for every wheel. I’ve been doodling, and will post on this over the next week or two.