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Movement Ratio given Number of Teeth on Pinion Formula

GoMovement Ratio Formula

GoMovement Ratio given Load and Effort Formula

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Movement Ratio is the ratio of the output movement to the input movement in a mechanical system. It indicates how much the system amplifies or reduces motion. Check FAQs

MR = 2 \cdot π \cdot \frac{r sw}{Z p \cdot p}

MR - Movement Ratio?r_sw - Radius of Steering Wheel?Z_p - Number of Teeth on Pinion?p - Circular Pitch of Pinion?π - Archimedes' constant?

Movement Ratio given Number of Teeth on Pinion Example

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Here is how the Movement Ratio given Number of Teeth on Pinion equation looks like with Values.

Here is how the Movement Ratio given Number of Teeth on Pinion equation looks like with Units.

Here is how the Movement Ratio given Number of Teeth on Pinion equation looks like.

15 = 2 \cdot 3.1416 \cdot \frac{150}{9 \cdot 6.9813}

15 = 2 \cdot 3.1416 \cdot \frac{150mm}{9 \cdot 6.9813mm}

15 = 2 \cdot 3.1416 \cdot \frac{150}{9 \cdot 6.9813}

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Movement Ratio given Number of Teeth on Pinion Solution

Follow our step by step solution on how to calculate Movement Ratio given Number of Teeth on Pinion?

FIRST Step Consider the formula

MR = 2 \cdot π \cdot \frac{r sw}{Z p \cdot p}

Next Step Substitute values of Variables

∴

MR = 2 \cdot π \cdot \frac{150mm}{9 \cdot 6.9813mm}

Next Step Substitute values of Constants

∴

MR = 2 \cdot 3.1416 \cdot \frac{150mm}{9 \cdot 6.9813mm}

Next Step Convert Units

∴

MR = 2 \cdot 3.1416 \cdot \frac{0.15m}{9 \cdot 0.007m}

Next Step Prepare to Evaluate

∴

MR = 2 \cdot 3.1416 \cdot \frac{0.15}{9 \cdot 0.007}

Next Step Evaluate

∴

MR = 14.9999999956541

LAST Step Rounding Answer

∴

MR = 15

Movement Ratio given Number of Teeth on Pinion Formula Elements

Variables

Constants

Movement Ratio

Movement Ratio is the ratio of the output movement to the input movement in a mechanical system. It indicates how much the system amplifies or reduces motion.

Symbol: MR

Measurement: NAUnit: Unitless

Note: Value should be greater than 0.

Formulas to find Movement Ratio

Radius of Steering Wheel

Radius of Steering Wheel is the distance from the center of the wheel to its edge. It affects the leverage and effort required to turn the steering wheel.

Symbol: r_sw

Measurement: LengthUnit: mm

Note: Value should be greater than 0.

Formulas to find Radius of Steering Wheel

Number of Teeth on Pinion

Number of Teeth on Pinion refers to the total count of gear teeth around its circumference.

Symbol: Z_p

Measurement: NAUnit: Unitless

Note: Value should be greater than 0.

Formulas to find Number of Teeth on Pinion

Circular Pitch of Pinion

Circular Pitch of Pinion is the distance between corresponding points on adjacent teeth, measured along the pitch circle.

Symbol: p

Measurement: LengthUnit: mm

Note: Value should be greater than 0.

Formulas to find Circular Pitch of Pinion

Archimedes' constant

Archimedes' constant is a mathematical constant that represents the ratio of the circumference of a circle to its diameter.

Symbol: π

Value: 3.14159265358979323846264338327950288

Other Formulas to find Movement Ratio

Go Movement Ratio

MR = \frac{r sw}{r}

Go Movement Ratio given Load and Effort

MR = \frac{W}{E}

Other formulas in Movement Ratio category

Go Radius of Steering Wheel given Movement Ratio

r sw = MR \cdot r

Go Radius of Pinion Pitch Circle given Movement Ratio

r = \frac{r sw}{MR}

Go Pinion Teeth given Movement Ratio

Z p = \frac{2 \cdot π \cdot r sw}{p \cdot MR}

Go Radius of Steering Wheel given Movement Ratio and Circular Pinion Pitch

r sw = \frac{MR}{2 \cdot \frac{π}{Z p \cdot p}}

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

Movement Ratio given Number of Teeth on Pinion evaluator uses Movement Ratio = 2*pi*Radius of Steering Wheel/(Number of Teeth on Pinion*Circular Pitch of Pinion) to evaluate the Movement Ratio, Movement Ratio given Number of Teeth on Pinion formula is defined as a dimensionless quantity that characterizes the gear ratio of a pair of gears, providing a relative measure of the rotational speed and torque between the pinion and the gear. It is an essential parameter in gear design and analysis, influencing the overall performance and efficiency of the mechanical system. Movement Ratio is denoted by MR symbol.

How to evaluate Movement Ratio given Number of Teeth on Pinion using this online evaluator? To use this online evaluator for Movement Ratio given Number of Teeth on Pinion, enter Radius of Steering Wheel (r_sw), Number of Teeth on Pinion (Z_p) & Circular Pitch of Pinion (p) and hit the calculate button.

FAQs on Movement Ratio given Number of Teeth on Pinion

What is the formula to find Movement Ratio given Number of Teeth on Pinion?

The formula of Movement Ratio given Number of Teeth on Pinion is expressed as Movement Ratio = 2*pi*Radius of Steering Wheel/(Number of Teeth on Pinion*Circular Pitch of Pinion). Here is an example- 15.00283 = 2*pi*0.15/(9*0.00698131701).

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

With Radius of Steering Wheel (r_sw), Number of Teeth on Pinion (Z_p) & Circular Pitch of Pinion (p) we can find Movement Ratio given Number of Teeth on Pinion using the formula - Movement Ratio = 2*pi*Radius of Steering Wheel/(Number of Teeth on Pinion*Circular Pitch of Pinion). This formula also uses Archimedes' constant .

What are the other ways to Calculate Movement Ratio?

Here are the different ways to Calculate Movement Ratio-

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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: Unit

Movement Ratio given Number of Teeth on Pinion Formula

​GoMovement Ratio Formula

​GoMovement Ratio given Load and Effort Formula

Movement Ratio given Number of Teeth on Pinion Example

Movement Ratio given Number of Teeth on Pinion Solution

Movement Ratio given Number of Teeth on Pinion Formula Elements

Other Formulas to find Movement Ratio

Other formulas in Movement Ratio category

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

FAQs on Movement Ratio given Number of Teeth on Pinion

Variable Name

GoMovement Ratio Formula

GoMovement Ratio given Load and Effort Formula