Page 245 - Robot Design Handbook ROBOCON Malaysia 2019

2.6 Calculations for the Placement of Omni-Wheels

Figure 8: Schematic of the three omni-wheels robot

Figure 8 shows the schematic view of the three omni-wheels robot, where each
wheel (W1, W2, W3) is 120 degrees apart. R is the length from the centre of the robot to

each wheel. VW1, VW2, VW3 are velocities of wheel 1, wheel 2 and wheel 3. r is the radius
of each omni-wheel. From the kinematics equation, all forces are divided into two

components which are the X-component and Y-component to X-axis and Y-axis

respectively. The following equations have been used in our robot design:

For wheel 1, W1,
2 =⁡− ( ) (1)
2
2 =⁡ ( ) (2)
2

For wheel 2, W2,

= 3 − ( ) − ( ) (3)
2
1
= ( ) − ( ) (4)
2
1
= 1 + 2 + 3 (5)

(1,2,3) = . (6)

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