View Single Post
  #26   Spotlight this post!  
Unread 10-05-2015, 10:43
GeeTwo's Avatar
GeeTwo GeeTwo is offline
Technical Director
AKA: Gus Michel II
FRC #3946 (Tiger Robotics)
Team Role: Mentor
 
Join Date: Jan 2014
Rookie Year: 2013
Location: Slidell, LA
Posts: 3,713
GeeTwo has a reputation beyond reputeGeeTwo has a reputation beyond reputeGeeTwo has a reputation beyond reputeGeeTwo has a reputation beyond reputeGeeTwo has a reputation beyond reputeGeeTwo has a reputation beyond reputeGeeTwo has a reputation beyond reputeGeeTwo has a reputation beyond reputeGeeTwo has a reputation beyond reputeGeeTwo has a reputation beyond reputeGeeTwo has a reputation beyond repute
Re: Kiwi Drive Concept

Combining the two transformations, to rotate an equilateral kiwi drive around a pivot point (xp, yp) with angular speed ω, the inverse kinematics using Ether's diagram above are:
S1 = ω * (r - yp)

S2 = ω * (r + 0.5*yp - 0.866*xp)

S3 = ω * (r + 0.5*yp + 0.866*xp)
Checking rotation points to verify that we didn't swap sign conventions along the way:

(0,0): all are ωr, check
(0,r): S1 = 0, S2 = S3 = 1.5ωr, reasonable
(0,2r): S1 = -ωr, S2 = S3 = 2ωr, reasonable
(0,-2r): S1 = 3ωr, S2 = S3 = 0, check
(1.155r, 0): S1 = ωr, S2 = 0, S3 = 2ωr, ok
(-1.155r, 0): S1 = ωr, S2 = 2ωr, S3 = 0, ok


If you want "forward" to be directly between wheels rather than through one (for example if you'll be picking up pieces or doing an internal stack), rotate the robot 180 degrees, leaving the axes and forward arrow in place. Then, the inverse kinematics for rotation about (xp, yp) become:
S1 = ω * (r + yp)

S2 = ω * (r - 0.5*yp + 0.866*xp)

S3 = ω * (r - 0.5*yp - 0.866*xp)
Attached Thumbnails
Click image for larger version

Name:	kiwi-inverse.png
Views:	39
Size:	16.4 KB
ID:	18986  
__________________

If you can't find time to do it right, how are you going to find time to do it over?
If you don't pass it on, it never happened.
Robots are great, but inspiration is the reason we're here.
Friends don't let friends use master links.

Last edited by GeeTwo : 10-05-2015 at 11:01.
Reply With Quote