# 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

## 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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