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Pinion Teeth given Movement Ratio Formula

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

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

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

Pinion Teeth given Movement Ratio Example

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

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

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

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

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

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

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Pinion Teeth given Movement Ratio Solution

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

FIRST Step Consider the formula

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

Next Step Substitute values of Variables

∴

Z p = \frac{2 \cdot π \cdot 150mm}{6.9813mm \cdot 15}

Next Step Substitute values of Constants

∴

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

Next Step Convert Units

∴

Z p = \frac{2 \cdot 3.1416 \cdot 0.15m}{0.007m \cdot 15}

Next Step Prepare to Evaluate

∴

Z p = \frac{2 \cdot 3.1416 \cdot 0.15}{0.007 \cdot 15}

Next Step Evaluate

∴

Z p = 8.99999999739245

LAST Step Rounding Answer

∴

Z p = 9

Pinion Teeth given Movement Ratio Formula Elements

Variables

Constants

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

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

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

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

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 in Movement Ratio category

Go Movement Ratio

MR = \frac{r sw}{r}

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 Movement Ratio given Number of Teeth on Pinion

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

How to Evaluate Pinion Teeth given Movement Ratio?

Pinion Teeth given Movement Ratio evaluator uses Number of Teeth on Pinion = (2*pi*Radius of Steering Wheel)/(Circular Pitch of Pinion*Movement Ratio) to evaluate the Number of Teeth on Pinion, Pinion Teeth given Movement Ratio formula is defined as the number of teeth on the pinion gear in a gear train system, which is a critical component in mechanical power transmission, and is determined by the movement ratio and other key parameters of the system. Number of Teeth on Pinion is denoted by Z_p symbol.

How to evaluate Pinion Teeth given Movement Ratio using this online evaluator? To use this online evaluator 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.

FAQs on Pinion Teeth given Movement Ratio

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

The formula of Pinion Teeth given Movement Ratio is expressed as Number of Teeth on Pinion = (2*pi*Radius of Steering Wheel)/(Circular Pitch of Pinion*Movement Ratio). Here is an example- 9.001698 = (2*pi*0.15)/(0.00698131701*15).

How to calculate Pinion Teeth given Movement Ratio?

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

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Pinion Teeth given Movement Ratio Formula

Pinion Teeth given Movement Ratio Example

Pinion Teeth given Movement Ratio Solution

Pinion Teeth given Movement Ratio Formula Elements

Other formulas in Movement Ratio category

How to Evaluate Pinion Teeth given Movement Ratio?

FAQs on Pinion Teeth given Movement Ratio

Variable Name