Frames for a KELO platform
Drive unit
Kinematically, each drive unit is the composition of (i) a differential drive; and (ii) a castor wheel. Each individual wheel features a hub-drive, i.e. the motor is placed inside a wheel to directly actuate its axle. This design implies that a drive unit is singularity-free, i.e. the two wheels can produce arbitrary (linear) forces at the pivot joint. The wheels and the pivot joint rotate around the positive \(z\) axis.
Frame diagram
Top-down view:
+x ^
|
+y |
<----+ [p]
o ^
+x ^ ^ | castor |
| | _ | _ offset |
+z | | | | | | | [r] |
<----o f[l] | |-+-| | f[r] o----> v
[l] |_| |_| | | +z
[c] left right | |
v v +x
|-----|
wheel distance
Coordinate frames’ axes
Frame |
Symbol |
\(x\) |
\(y\) |
\(z\) |
|---|---|---|---|---|
Left wheel |
[l] |
front |
down |
left |
Right wheel |
[r] |
rear |
down |
right |
Centre |
[c] |
front |
down |
right |
Pivot |
[p] |
front |
left |
up |
Coordinate frames’ origins
Symbol |
\(x\) |
\(y\) |
\(z\) |
|---|---|---|---|
[l] |
on axle |
wheel centre |
wheel centre |
[r] |
on axle |
wheel centre |
wheel centre |
[c] |
on axle |
wheel centre |
centre between wheels |
[p] |
on pivot joint axis |
on pivot joint axis |
— |
Platform
Drive units are ordered in mathematically positive direction (counter-clockwise in the top-down view), starting at the front-left wheel. The positive direction of the pivot joints (in the top-down view) is clockwise, i.e. the pivot joints rotate around the positive \(z\) axis.
Top-down view:
+x ^
| W1 |-| |-| W4
| | |
<----+ o--------o ^ +x
+y [a] | | |
| | |
| | <----+ [p]
| | +y
o--------o
| |
W2 |-| |-| W3
Coordinate frames’ axes
Frame |
Symbol |
\(x\) |
\(y\) |
\(z\) |
|---|---|---|---|---|
Platform |
[p] |
front |
left |
up |
Attachment |
[a] |
front |
left |
up |
Coordinate frames’ origins
Symbol |
\(x\) |
\(y\) |
\(z\) |
|---|---|---|---|
[p] |
platform centre |
platform centre |
— |
[a] |
on pivot joint axis |
on pivot joint axis |
— |