Calculating Wheel Movement for Accurate Turns

Overview:

  • Two Types of Turns
  • Calculating Rotations for Pivot Turns
  • Equation for Calculating Pivot Turns
  • Calculating Rotations for Point Turns
  • Equation for Calculating Point Turns
  • Relationships Between the Two Types of Turns
  • Parting Thoughts

Two Types of Turns:

  • Pivot Turn – robot turns about a central point located at one of the wheels
  • One wheel goes forward, or reverse, while the other does not rotate
  • Left wheel forward is a right turn and vice versa
  • Left wheel reverse is a left turn and vice versa

    • Point Turn – robot turns about a central point located midway between the wheels
    • One wheel goes forward while the other goes in reverse
    • Left wheel forward, right wheel reverse is a right turn
    • Right wheel forward, left wheel reverse is a left turn

Calculating Rotations for Pivot Turns:

In this example we want a 180° right pivot turn

  • Left wheel forward, right wheel stationary
  • The left wheel will follow the blue circular path
  • The diameter of this path = 2 times the width from wheel center to wheel center, or track width
  • The circumference of a full circular path is: circumference = π x 2 x track width
  • Since we are travelling only 180° (half) of the 360° that make up a circle, we multiply the circumference by 180°/360° (1/2) to get the length of the path the robot will travel
  • The last step is to divide by the circumference of the wheel to get the rotations needed

Equation for Calculating Pivot Turns:

  • For an n degree pivot turn
  • Rot= n⁄360×((2×W_t×π))/C_w
  • Where
    • Rot = rotations
    • n = degree of turn
    • W_t = track width
    • C_w = circumference of wheel

Calculating Rotations for Point Turns:

In this example we want a 180° right point turn:

  • -Left wheel forward, right wheel reverse
  • -The left wheel will follow the blue circular path, the right wheel will follow the red circular path
  • -The diameter of this path = the width from wheel center to wheel center, or track width
  • -The circumference of a full circular path is: circumference = π x track width
  • -Since we are travelling only 180° (half) of the 360° that make up a circle, we multiply the circumference by 180°/360° (1/2) to get the length of the path the robot will travel
  • -The last step is to divide by the circumference of the wheel to get the rotations needed

Equation for Calculating Pivot Turns:

  • For an ‘n’ degree pivot turn
  • Rot= n⁄360×((W_t×π))/C_w
  • Where
    • Rot = rotations
    • n = degree of turn
    • W_t = track width
    • C_w = circumference of wheel

Code for Pivot Turn In Rotations:

Download Code: PivotTurn in ‘n’ Rotations.ev3s

Code for Pivot Turn In Degrees:

Download Code: PivotTurn in ‘n’ Degrees.ev3s


Relationships Between the Two Types of Turns:

Pivot Turns:

  • Need twice as many rotations as a point turn
  • Need more space
  • More forgiving* of errors

Point Turns:

  • Need half as many rotations as a pivot turn
  • Need less space
  • Less forgiving* of errors

*Forgiving meaning that an error in calculation is a smaller percentage of the total rotations needed.

Parting Thoughts:

  • The process used for finding the path is the same process used to find the arc length of a circle in geometry, we just divide the arc length by the wheel circumference to find wheel rotations.
  • The pivot turn does twice as many rotations as a point turn because only one wheel is doing the turning. In a point turn both wheels are turning so they each turn only half as many rotations as a pivot turn to turn the robot the same number of degrees.

 

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