Pinion Teeth given Movement Ratio Calculator

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Front Axle and Steering

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Race Car Vehicle Dynamics

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Movement Ratio

Moments, Loads, Angles acting on Steering system and Axles

Pivot Centre, Wheel Base and Track

Steering System

Turning Radius

✖The Radius of Steering Wheel is the distance from the center of the steering wheel to the outermost point.ⓘ Radius of Steering Wheel [r_sw]			+10% -10%
✖Circular Pitch of Pinion is the distance along the pitch circle or pitch line between corresponding profiles of adjacent teeth.ⓘ Circular Pitch of Pinion [p]			+10% -10%
✖Movement Ratio is defined as the ratio of the distance moved by the effort to the distance moved by the load.ⓘ Movement Ratio [MR]			+10% -10%

✖Number of Teeth on Pnion is the count of teeth on pinion.ⓘ Pinion Teeth given Movement Ratio [Z_p]

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Formula

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Pinion Teeth given Movement Ratio

Formula

`"Z"_{"p"} = 2*pi*"r"_{"sw"}/("p"*"MR")`

Example

`"12.56637"=2*pi*"150mm"/("5mm"*"15")`

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Download Front Axle and Steering Formula PDF

Pinion Teeth given Movement Ratio Solution

STEP 0: Pre-Calculation Summary

Formula Used

Number of Teeth on Pnion = 2*pi*Radius of Steering Wheel/(Circular Pitch of Pinion*Movement Ratio)
Z_p = 2*pi*r_sw/(p*MR)
This formula uses 1 Constants, 4 Variables

Constants Used

pi - Archimedes' constant Value Taken As 3.14159265358979323846264338327950288

Variables Used

Number of Teeth on Pnion - Number of Teeth on Pnion is the count of teeth on pinion.
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.
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.
Movement Ratio - Movement Ratio is defined as the ratio of the distance moved by the effort to the distance moved by the load.

STEP 1: Convert Input(s) to Base Unit

Radius of Steering Wheel: 150 Millimeter --> 0.15 Meter (Check conversion here)
Circular Pitch of Pinion: 5 Millimeter --> 0.005 Meter (Check conversion here)
Movement Ratio: 15 --> No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

Z_p = 2*pi*r_sw/(p*MR) --> 2*pi*0.15/(0.005*15)

Evaluating ... ...

Z_p = 12.5663706143592

STEP 3: Convert Result to Output's Unit

12.5663706143592 --> No Conversion Required

FINAL ANSWER

12.5663706143592 ≈ 12.56637 <-- Number of Teeth on Pnion

(Calculation completed in 00.004 seconds)

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Credits

Created by Peri Krishna Karthik

National Institute of Technology Calicut (NIT Calicut), Calicut, Kerala

Peri Krishna Karthik has created this Calculator and 200+ more calculators!

Verified by sanjay shiva

national institute of technology hamirpur (NITH ), hamirpur , himachal pradesh

sanjay shiva has verified this Calculator and 100+ more calculators!

< 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

Pinion Teeth given Movement Ratio Formula

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

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 Pinion Teeth given Movement Ratio?

Pinion Teeth given Movement Ratio calculator uses Number of Teeth on Pnion = 2*pi*Radius of Steering Wheel/(Circular Pitch of Pinion*Movement Ratio) to calculate the Number of Teeth on Pnion, The Pinion teeth given movement ratio formula is used to find the count of teeth on pinion. Number of Teeth on Pnion is denoted by Z_p symbol.

How to calculate Pinion Teeth given Movement Ratio using this online calculator? To use this online calculator for Pinion Teeth given Movement Ratio, enter Radius of Steering Wheel (r_sw), Circular Pitch of Pinion (p) & Movement Ratio (MR) and hit the calculate button. Here is how the Pinion Teeth given Movement Ratio calculation can be explained with given input values -> 12.56637 = 2*pi*0.15/(0.005*15).

FAQ

What is Pinion Teeth given Movement Ratio?

The Pinion teeth given movement ratio formula is used to find the count of teeth on pinion and is represented as Z_p = 2*pi*r_sw/(p*MR) or Number of Teeth on Pnion = 2*pi*Radius of Steering Wheel/(Circular Pitch of Pinion*Movement Ratio). The Radius of Steering Wheel is the distance from the center of the steering wheel to the outermost point, Circular Pitch of Pinion is the distance along the pitch circle or pitch line between corresponding profiles of adjacent teeth & Movement Ratio is defined as the ratio of the distance moved by the effort to the distance moved by the load.

How to calculate Pinion Teeth given Movement Ratio?

The Pinion teeth given movement ratio formula is used to find the count of teeth on pinion is calculated using Number of Teeth on Pnion = 2*pi*Radius of Steering Wheel/(Circular Pitch of Pinion*Movement Ratio). To calculate Pinion Teeth given Movement Ratio, you need Radius of Steering Wheel (r_sw), Circular Pitch of Pinion (p) & Movement Ratio (MR). With our tool, you need to enter the respective value for Radius of Steering Wheel, Circular Pitch of Pinion & Movement Ratio and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.

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