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Angle between Two Arms of Rocker Arm Formula

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Angle Between Rocker Arms is the angle between the two arms of a rocker arm or the contained angle between the rocker arms. Check FAQs

θ = π - \arccos (- \frac{{P e}^{2} + {P c}^{2} - {R f}^{2}}{2 \cdot P e \cdot P c})

θ - Angle Between Rocker Arms?P_e - Total Force on Rocker Arm of Exhaust Valve?P_c - Force on Roller Pin?R_f - Force at Fulcrum Pin?π - Archimedes' constant?

Angle between Two Arms of Rocker Arm Example

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Here is how the Angle between Two Arms of Rocker Arm equation looks like with Values.

Here is how the Angle between Two Arms of Rocker Arm equation looks like with Units.

Here is how the Angle between Two Arms of Rocker Arm equation looks like.

135.1667 = 3.1416 - \arccos (- \frac{1926^{2} + 1925^{2} - 3560^{2}}{2 \cdot 1926 \cdot 1925})

135.1667° = 3.1416 - \arccos (- \frac{{1926N}^{2} + {1925N}^{2} - {3560N}^{2}}{2 \cdot 1926N \cdot 1925N})

135.1667 = 3.1416 - \arccos (- \frac{1926^{2} + 1925^{2} - 3560^{2}}{2 \cdot 1926 \cdot 1925})

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Angle between Two Arms of Rocker Arm Solution

Follow our step by step solution on how to calculate Angle between Two Arms of Rocker Arm?

FIRST Step Consider the formula

θ = π - \arccos (- \frac{{P e}^{2} + {P c}^{2} - {R f}^{2}}{2 \cdot P e \cdot P c})

Next Step Substitute values of Variables

∴

θ = π - \arccos (- \frac{{1926N}^{2} + {1925N}^{2} - {3560N}^{2}}{2 \cdot 1926N \cdot 1925N})

Next Step Substitute values of Constants

∴

θ = 3.1416 - \arccos (- \frac{{1926N}^{2} + {1925N}^{2} - {3560N}^{2}}{2 \cdot 1926N \cdot 1925N})

Next Step Prepare to Evaluate

∴

θ = 3.1416 - \arccos (- \frac{1926^{2} + 1925^{2} - 3560^{2}}{2 \cdot 1926 \cdot 1925})

Next Step Evaluate

∴

θ = 2.35910369068687rad

Next Step Convert to Output's Unit

∴

θ = 135.166684910119°

LAST Step Rounding Answer

∴

θ = 135.1667°

Angle between Two Arms of Rocker Arm Formula Elements

Variables

Constants

Functions

Angle Between Rocker Arms

Angle Between Rocker Arms is the angle between the two arms of a rocker arm or the contained angle between the rocker arms.

Symbol: θ

Measurement: AngleUnit: °

Note: Value should be greater than 0.

Formulas to find Angle Between Rocker Arms

Total Force on Rocker Arm of Exhaust Valve

Total Force on Rocker Arm of Exhaust Valve is the total force acting onto the rocker arm of the exhaust valve.

Symbol: P_e

Measurement: ForceUnit: N

Note: Value should be greater than 0.

Formulas to find Total Force on Rocker Arm of Exhaust Valve

Force on Roller Pin

Force on Roller Pin is the force acting onto the roller pin ( the pivot about which a lever rolls freely) used as a joint.

Symbol: P_c

Measurement: ForceUnit: N

Note: Value should be greater than 0.

Formulas to find Force on Roller Pin

Force at Fulcrum Pin

Force at Fulcrum Pin is the force acting onto the fulcrum pin (the pivot about which a lever turns) used as a joint at a fulcrum point.

Symbol: R_f

Measurement: ForceUnit: N

Note: Value should be greater than 0.

Formulas to find Force at Fulcrum Pin

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

cos

Cosine of an angle is the ratio of the side adjacent to the angle to the hypotenuse of the triangle.

Syntax: cos(Angle)

arccos

Arccosine function, is the inverse function of the cosine function.It is the function that takes a ratio as an input and returns the angle whose cosine is equal to that ratio.

Syntax: arccos(Number)

Other formulas in Design of Fulcrum Pin category

Go Reaction at Fulcrum Pin of Rocker Arm

R f = \sqrt{{P e}^{2} + {P c}^{2} - 2 \cdot P c \cdot P e \cdot \cos (θ)}

Go Reaction at Fulcrum Pin of Rocker Arm for Equal Arm Lengths

R f = P e \cdot \sqrt{2 \cdot (1 - \cos (θ))}

Go Bearing Pressure at Fulcrum Pin of Rocker Arm

P bf = \frac{R f}{d 1 \cdot l 1}

Go Reaction at Fulcrum Pin of Rocker Arm Considering bearing Pressure

R f = d 1 \cdot l 1 \cdot P bf

How to Evaluate Angle between Two Arms of Rocker Arm?

Angle between Two Arms of Rocker Arm evaluator uses Angle Between Rocker Arms = pi-arccos(-(Total Force on Rocker Arm of Exhaust Valve^2+Force on Roller Pin^2-Force at Fulcrum Pin^2)/(2*Total Force on Rocker Arm of Exhaust Valve*Force on Roller Pin)) to evaluate the Angle Between Rocker Arms, The Angle between two arms of rocker arm is the angle between the two arms of a rocker arm or the contained angle between the rocker arms of an IC Engine valve mechanism. Angle Between Rocker Arms is denoted by θ symbol.

How to evaluate Angle between Two Arms of Rocker Arm using this online evaluator? To use this online evaluator for Angle between Two Arms of Rocker Arm, enter Total Force on Rocker Arm of Exhaust Valve (P_e), Force on Roller Pin (P_c) & Force at Fulcrum Pin (R_f) and hit the calculate button.

FAQs on Angle between Two Arms of Rocker Arm

What is the formula to find Angle between Two Arms of Rocker Arm?

The formula of Angle between Two Arms of Rocker Arm is expressed as Angle Between Rocker Arms = pi-arccos(-(Total Force on Rocker Arm of Exhaust Valve^2+Force on Roller Pin^2-Force at Fulcrum Pin^2)/(2*Total Force on Rocker Arm of Exhaust Valve*Force on Roller Pin)). Here is an example- 7744.481 = pi-arccos(-(1926^2+1925^2-3560^2)/(2*1926*1925)).

How to calculate Angle between Two Arms of Rocker Arm?

With Total Force on Rocker Arm of Exhaust Valve (P_e), Force on Roller Pin (P_c) & Force at Fulcrum Pin (R_f) we can find Angle between Two Arms of Rocker Arm using the formula - Angle Between Rocker Arms = pi-arccos(-(Total Force on Rocker Arm of Exhaust Valve^2+Force on Roller Pin^2-Force at Fulcrum Pin^2)/(2*Total Force on Rocker Arm of Exhaust Valve*Force on Roller Pin)). This formula also uses Archimedes' constant and , Cosine (cos), Inverse Cosine (arccos) function(s).

Can the Angle between Two Arms of Rocker Arm be negative?

No, the Angle between Two Arms of Rocker Arm, measured in Angle cannot be negative.

Which unit is used to measure Angle between Two Arms of Rocker Arm?

Angle between Two Arms of Rocker Arm is usually measured using the Degree[°] for Angle. Radian[°], Minute[°], Second[°] are the few other units in which Angle between Two Arms of Rocker Arm can be measured.

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Angle between Two Arms of Rocker Arm Formula

Angle between Two Arms of Rocker Arm Example

Angle between Two Arms of Rocker Arm Solution

Angle between Two Arms of Rocker Arm Formula Elements

Other formulas in Design of Fulcrum Pin category

How to Evaluate Angle between Two Arms of Rocker Arm?

FAQs on Angle between Two Arms of Rocker Arm

Variable Name