Question #6143

# How to convert radians to millimeters?

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Answer

You can't actually convert radians to millimeters. Radian is a measure of angle, while millimeters is a unit of distance. There is an homogeneity issue between the two quantities.

However, there are many mechanical systems that transform rotary motion into linear motion. The most obvious system is the wheel: the rotation of the wheel moves the vehicle forward and vice versa. In this case, the formula governing such a system and allowing to transform a rotation of an angle expressed in radians into a displacement given in millimeters is given by:

﻿﻿

﻿﻿

with :

• ﻿﻿ the distance or length expressed in millimetres [mm]
• ﻿﻿ is the radius expressed in metres [m]
• ﻿﻿ is the rotation angle expressed in radians [rad]

Take the example of a vehicle equipped with wheels with a radius of 0.25 mm (50 cm in diameter). Assume the wheel makes 3 turns, we can calculate the distance traveled by the vehicle. The angle of rotation of the wheel is 3 turns x 2π = 6π radians. The distance is therefore:

﻿﻿

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