Angle between Two Arms of Rocker Arm Calculator

✖Total Force on Rocker Arm of Exhaust Valve is the total force acting onto the rocker arm of the exhaust valve.ⓘ Total Force on Rocker Arm of Exhaust Valve [P_e]			+10% -10%
✖Force on Roller Pin is the force acting onto the roller pin ( the pivot about which a lever rolls freely) used as a joint.ⓘ Force on Roller Pin [P_c]			+10% -10%
✖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.ⓘ Force at Fulcrum Pin [R_f]			+10% -10%

✖Angle Between Rocker Arms is the angle between the two arms of a rocker arm or the contained angle between the rocker arms.ⓘ Angle between Two Arms of Rocker Arm [θ]

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Formula

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Angle between Two Arms of Rocker Arm

Formula

`"θ" = pi-arccos(-("P"_{"e"}^2+"P"_{"c"}^2-"R"_{"f"}^2)/(2*"P"_{"e"}*"P"_{"c"}))`

Example

`"135.1667°"=pi-arccos(-(("1926N")^2+("1925N")^2-("3560N")^2)/(2*"1926N"*"1925N"))`

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Angle between Two Arms of Rocker Arm Solution

STEP 0: Pre-Calculation Summary

Formula Used

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))
θ = pi-arccos(-(P_e^2+P_c^2-R_f^2)/(2*P_e*P_c))
This formula uses 1 Constants, 2 Functions, 4 Variables

Constants Used

pi - Archimedes' constant Value Taken As 3.14159265358979323846264338327950288

Functions Used

cos - Cosine of an angle is the ratio of the side adjacent to the angle to the hypotenuse of the triangle., 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., arccos(Number)

Variables Used

Angle Between Rocker Arms - (Measured in Radian) - Angle Between Rocker Arms is the angle between the two arms of a rocker arm or the contained angle between the rocker arms.
Total Force on Rocker Arm of Exhaust Valve - (Measured in Newton) - Total Force on Rocker Arm of Exhaust Valve is the total force acting onto the rocker arm of the exhaust valve.
Force on Roller Pin - (Measured in Newton) - Force on Roller Pin is the force acting onto the roller pin ( the pivot about which a lever rolls freely) used as a joint.
Force at Fulcrum Pin - (Measured in Newton) - 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.

STEP 1: Convert Input(s) to Base Unit

Total Force on Rocker Arm of Exhaust Valve: 1926 Newton --> 1926 Newton No Conversion Required
Force on Roller Pin: 1925 Newton --> 1925 Newton No Conversion Required
Force at Fulcrum Pin: 3560 Newton --> 3560 Newton No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

θ = pi-arccos(-(P_e^2+P_c^2-R_f^2)/(2*P_e*P_c)) --> pi-arccos(-(1926^2+1925^2-3560^2)/(2*1926*1925))

Evaluating ... ...

θ = 2.35910369068687

STEP 3: Convert Result to Output's Unit

2.35910369068687 Radian -->135.166684910119 Degree (Check conversion here)

FINAL ANSWER

135.166684910119 ≈ 135.1667 Degree <-- Angle Between Rocker Arms

(Calculation completed in 00.004 seconds)

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Home » Physics » IC Engine » Design of IC Engine Components » Rocker Arm » Design of Fulcrum Pin » Angle between Two Arms of Rocker Arm

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Shri Govindram Seksaria Institute of Technology and Science (SGSITS ), Indore

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< 17 Design of Fulcrum Pin Calculators

Length of Fulcrum Pin of Rocker Arm considering Double Shear Failure of Pin

Go Length of Fulcrum Pin = 1.25*sqrt((2*sqrt(Total Force on Rocker Arm of Exhaust Valve^2+Force on Roller Pin^2-2*Force on Roller Pin*Total Force on Rocker Arm of Exhaust Valve*cos(Angle Between Rocker Arms)))/(pi*Shear Stress in Fulcrum Pin))

Diameter of Fulcrum Pin of Rocker Arm Considering Double Shear Failure of Pin

Go Diameter of Fulcrum Pin = sqrt((2*sqrt(Total Force on Rocker Arm of Exhaust Valve^2+Force on Roller Pin^2-2*Force on Roller Pin*Total Force on Rocker Arm of Exhaust Valve*cos(Angle Between Rocker Arms)))/(pi*Shear Stress in Fulcrum Pin))

Shear Stress in Fulcrum Pin of Rocker Arm

Go Shear Stress in Fulcrum Pin = (2*(sqrt(Total Force on Rocker Arm of Exhaust Valve^2+Force on Roller Pin^2-2*Force on Roller Pin*Total Force on Rocker Arm of Exhaust Valve*cos(Angle Between Rocker Arms)))/(pi*Diameter of Fulcrum Pin^2))

Angle between Two Arms of Rocker Arm

Go 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))

Reaction at Fulcrum Pin of Rocker Arm

Go Force at Fulcrum Pin = sqrt(Total Force on Rocker Arm of Exhaust Valve^2+Force on Roller Pin^2-2*Force on Roller Pin*Total Force on Rocker Arm of Exhaust Valve*cos(Angle Between Rocker Arms))

Reaction at Fulcrum Pin of Rocker Arm for Equal Arm Lengths

Go Force at Fulcrum Pin = Total Force on Rocker Arm of Exhaust Valve*sqrt(2*(1-cos(Angle Between Rocker Arms)))

Length of Fulcrum Pin of Rocker Arm given Reaction at Pin

Go Length of Fulcrum Pin = 1.25*sqrt((2*Force at Fulcrum Pin)/(pi*Shear Stress in Fulcrum Pin))

Diameter of Fulcrum Pin of Rocker Arm given Reaction at Pin

Go Diameter of Fulcrum Pin = sqrt((2*Force at Fulcrum Pin)/(pi*Shear Stress in Fulcrum Pin))

Bearing Pressure at Fulcrum Pin of Rocker Arm

Go Bearing Pressure for Fulcrum Pin = (Force at Fulcrum Pin)/(Diameter of Fulcrum Pin*Length of Fulcrum Pin)

Diameter of Fulcrum Pin of Rocker Arm given Bearing Pressure

Go Diameter of Fulcrum Pin = Force at Fulcrum Pin/(Length of Fulcrum Pin*Bearing Pressure for Fulcrum Pin)

Length of Fulcrum Pin of Rocker Arm given Bearing Pressure

Go Length of Fulcrum Pin = Force at Fulcrum Pin/(Diameter of Fulcrum Pin*Bearing Pressure for Fulcrum Pin)

Reaction at Fulcrum Pin of Rocker Arm Considering bearing Pressure

Go Force at Fulcrum Pin = Diameter of Fulcrum Pin*Length of Fulcrum Pin*Bearing Pressure for Fulcrum Pin

Shear Stress in Fulcrum Pin of Rocker Arm given Reaction at Pin

Go Shear Stress in Fulcrum Pin = (2*Force at Fulcrum Pin)/(pi*Diameter of Fulcrum Pin^2)

Reaction at Fulcrum Pin of Rocker Arm considering Double Shear Failure of Pin

Go Force at Fulcrum Pin = (Shear Stress in Fulcrum Pin*pi*Diameter of Fulcrum Pin^2)/2

Outside Diameter of Boss of Rocker Arm at Fulcrum Pin

Go Outside Diameter of Boss of Rocker Arm = 2*Diameter of Fulcrum Pin

Length of Fulcrum Pin of Rocker Arm given Diameter of Fulcrum Pin

Go Length of Fulcrum Pin = Diameter of Fulcrum Pin*1.25

Diameter of Fulcrum Pin of Rocker Arm given Length of Fulcrum Pin

Go Diameter of Fulcrum Pin = Length of Fulcrum Pin/1.25

Angle between Two Arms of Rocker Arm Formula

Forces acting on rocker arm

(i) The gas pressure on the valve when it opens.
(ii) The inertia force when the valve moves up.
(iii) The initial spring force to hold the valve on its seat against suction or negative pressure inside the cylinder during the suction stroke.

How to Calculate Angle between Two Arms of Rocker Arm?

Angle between Two Arms of Rocker Arm calculator 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 calculate 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 calculate Angle between Two Arms of Rocker Arm using this online calculator? To use this online calculator 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. Here is how the Angle between Two Arms of Rocker Arm calculation can be explained with given input values -> 7744.481 = pi-arccos(-(1926^2+1925^2-3560^2)/(2*1926*1925)).

FAQ

What is Angle between Two Arms of Rocker Arm?

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 and is represented as θ = pi-arccos(-(P_e^2+P_c^2-R_f^2)/(2*P_e*P_c)) or 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)). Total Force on Rocker Arm of Exhaust Valve is the total force acting onto the rocker arm of the exhaust valve, Force on Roller Pin is the force acting onto the roller pin ( the pivot about which a lever rolls freely) used as a joint & 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.

How to calculate Angle between Two Arms of Rocker Arm?

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 is calculated using 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 calculate Angle between Two Arms of Rocker Arm, you need Total Force on Rocker Arm of Exhaust Valve (P_e), Force on Roller Pin (P_c) & Force at Fulcrum Pin (R_f). With our tool, you need to enter the respective value for Total Force on Rocker Arm of Exhaust Valve, Force on Roller Pin & Force at Fulcrum Pin 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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