Movement Ratio given Number of Teeth on Pinion Solution

STEP 0: Pre-Calculation Summary
Formula Used
Movement Ratio = 2*pi*Radius of Steering Wheel/(Number of Teeth on Pnion*Circular Pitch of Pinion)
MR = 2*pi*rsw/(Zp*p)
This formula uses 1 Constants, 4 Variables
Constants Used
pi - Archimedes' constant Value Taken As 3.14159265358979323846264338327950288
Variables Used
Movement Ratio - Movement Ratio is defined as the ratio of the distance moved by the effort to the distance moved by the load.
Radius of Steering Wheel - (Measured in Meter) - The Radius of Steering Wheel is the distance from the center of the steering wheel to the outermost point.
Number of Teeth on Pnion - Number of Teeth on Pnion is the count of teeth on pinion.
Circular Pitch of Pinion - (Measured in Meter) - Circular Pitch of Pinion is the distance along the pitch circle or pitch line between corresponding profiles of adjacent teeth.
STEP 1: Convert Input(s) to Base Unit
Radius of Steering Wheel: 150 Millimeter --> 0.15 Meter (Check conversion here)
Number of Teeth on Pnion: 9 --> No Conversion Required
Circular Pitch of Pinion: 5 Millimeter --> 0.005 Meter (Check conversion here)
STEP 2: Evaluate Formula
Substituting Input Values in Formula
MR = 2*pi*rsw/(Zp*p) --> 2*pi*0.15/(9*0.005)
Evaluating ... ...
MR = 20.943951023932
STEP 3: Convert Result to Output's Unit
20.943951023932 --> No Conversion Required
FINAL ANSWER
20.943951023932 20.94395 <-- Movement Ratio
(Calculation completed in 00.004 seconds)

Credits

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9 Movement Ratio Calculators

Radius of Steering Wheel given Movement Ratio and Circular Pinion Pitch
Go Radius of Steering Wheel = Movement Ratio/(2*pi/(Number of Teeth on Pnion*Circular Pitch of Pinion))
Movement Ratio given Number of Teeth on Pinion
Go Movement Ratio = 2*pi*Radius of Steering Wheel/(Number of Teeth on Pnion*Circular Pitch of Pinion)
Pinion Teeth given Movement Ratio
Go Number of Teeth on Pnion = 2*pi*Radius of Steering Wheel/(Circular Pitch of Pinion*Movement Ratio)
Radius of Pinion Pitch Circle given Movement Ratio
Go Radius of Pitch Circle of Pinion = Radius of Steering Wheel/Movement Ratio
Radius of Steering Wheel given Movement Ratio
Go Radius of Steering Wheel = Movement Ratio*Radius of Pitch Circle of Pinion
Movement Ratio
Go Movement Ratio = Radius of Steering Wheel/Radius of Pitch Circle of Pinion
Input Effort at Steering Wheel given Movement Ratio
Go Input Effort at Stepping Wheel = Output Load at Rack/Movement Ratio
Output Load at Rack given Movement Ratio
Go Output Load at Rack = Movement Ratio*Input Effort at Stepping Wheel
Movement Ratio given Load and Effort
Go Movement Ratio = Output Load at Rack/Input Effort at Stepping Wheel

Movement Ratio given Number of Teeth on Pinion Formula

Movement Ratio = 2*pi*Radius of Steering Wheel/(Number of Teeth on Pnion*Circular Pitch of Pinion)
MR = 2*pi*rsw/(Zp*p)

Rack and Pinion Steering System

It is used on light vehicles like cars and in power steering. It is simple, light and responsive and occupies a very small space and used a lesser number of linkage components compared to the worm and wheel type of gear. The rotary movement of steering wheel is transmitted with rack. The circular motion of the pinion is transformed into linear rack movement, which is further relayed through ball joints and tie rods to the stub axles for the wheels to be steered.

How to Calculate Movement Ratio given Number of Teeth on Pinion?

Movement Ratio given Number of Teeth on Pinion calculator uses Movement Ratio = 2*pi*Radius of Steering Wheel/(Number of Teeth on Pnion*Circular Pitch of Pinion) to calculate the Movement Ratio, The Movement Ratio given Number of Teeth on Pinion formula is used to find the ratio of the distance moved by the effort to the distance moved by the load. Movement Ratio is denoted by MR symbol.

How to calculate Movement Ratio given Number of Teeth on Pinion using this online calculator? To use this online calculator for Movement Ratio given Number of Teeth on Pinion, enter Radius of Steering Wheel (rsw), Number of Teeth on Pnion (Zp) & Circular Pitch of Pinion (p) and hit the calculate button. Here is how the Movement Ratio given Number of Teeth on Pinion calculation can be explained with given input values -> 20.94395 = 2*pi*0.15/(9*0.005).

FAQ

What is Movement Ratio given Number of Teeth on Pinion?
The Movement Ratio given Number of Teeth on Pinion formula is used to find the ratio of the distance moved by the effort to the distance moved by the load and is represented as MR = 2*pi*rsw/(Zp*p) or Movement Ratio = 2*pi*Radius of Steering Wheel/(Number of Teeth on Pnion*Circular Pitch of Pinion). The Radius of Steering Wheel is the distance from the center of the steering wheel to the outermost point, Number of Teeth on Pnion is the count of teeth on pinion & Circular Pitch of Pinion is the distance along the pitch circle or pitch line between corresponding profiles of adjacent teeth.
How to calculate Movement Ratio given Number of Teeth on Pinion?
The Movement Ratio given Number of Teeth on Pinion formula is used to find the ratio of the distance moved by the effort to the distance moved by the load is calculated using Movement Ratio = 2*pi*Radius of Steering Wheel/(Number of Teeth on Pnion*Circular Pitch of Pinion). To calculate Movement Ratio given Number of Teeth on Pinion, you need Radius of Steering Wheel (rsw), Number of Teeth on Pnion (Zp) & Circular Pitch of Pinion (p). With our tool, you need to enter the respective value for Radius of Steering Wheel, Number of Teeth on Pnion & Circular Pitch of Pinion and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.
How many ways are there to calculate Movement Ratio?
In this formula, Movement Ratio uses Radius of Steering Wheel, Number of Teeth on Pnion & Circular Pitch of Pinion. We can use 2 other way(s) to calculate the same, which is/are as follows -
  • Movement Ratio = Radius of Steering Wheel/Radius of Pitch Circle of Pinion
  • Movement Ratio = Output Load at Rack/Input Effort at Stepping Wheel
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