Reaction at Fulcrum Pin 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%
✖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 Rocker Arms [θ]			+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.ⓘ Reaction at Fulcrum Pin of Rocker Arm [R_f]

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Formula

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Reaction at Fulcrum Pin of Rocker Arm

Formula

`"R"_{"f"} = sqrt("P"_{"e"}^2+"P"_{"c"}^2-2*"P"_{"c"}*"P"_{"e"}*cos("θ"))`

Example

`"3557.86N"=sqrt(("1926N")^2+("1925N")^2-2*"1925N"*"1926N"*cos("135°"))`

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Reaction at Fulcrum Pin of Rocker Arm Solution

STEP 0: Pre-Calculation Summary

Formula Used

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))
R_f = sqrt(P_e^2+P_c^2-2*P_c*P_e*cos(θ))
This formula uses 2 Functions, 4 Variables

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)
sqrt - A square root function is a function that takes a non-negative number as an input and returns the square root of the given input number., sqrt(Number)

Variables Used

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.
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.
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.

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
Angle Between Rocker Arms: 135 Degree --> 2.3561944901919 Radian (Check conversion here)

STEP 2: Evaluate Formula

Substituting Input Values in Formula

R_f = sqrt(P_e^2+P_c^2-2*P_c*P_e*cos(θ)) --> sqrt(1926^2+1925^2-2*1925*1926*cos(2.3561944901919))

Evaluating ... ...

R_f = 3557.86010028135

STEP 3: Convert Result to Output's Unit

3557.86010028135 Newton --> No Conversion Required

FINAL ANSWER

3557.86010028135 ≈ 3557.86 Newton <-- Force at Fulcrum Pin

(Calculation completed in 00.004 seconds)

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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

Reaction at Fulcrum Pin 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 Reaction at Fulcrum Pin of Rocker Arm?

Reaction at Fulcrum Pin of Rocker Arm calculator uses 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)) to calculate the Force at Fulcrum Pin, The Reaction at fulcrum pin of rocker arm is the reaction force acting onto the fulcrum pin ( the pivot about which a lever turns) used as a joint at a fulcrum point, as a result of force due to exhaust valve reaction and force on the roller pin. Force at Fulcrum Pin is denoted by R_f symbol.

How to calculate Reaction at Fulcrum Pin of Rocker Arm using this online calculator? To use this online calculator for Reaction at Fulcrum Pin of Rocker Arm, enter Total Force on Rocker Arm of Exhaust Valve (P_e), Force on Roller Pin (P_c) & Angle Between Rocker Arms (θ) and hit the calculate button. Here is how the Reaction at Fulcrum Pin of Rocker Arm calculation can be explained with given input values -> 3557.86 = sqrt(1926^2+1925^2-2*1925*1926*cos(2.3561944901919)).

FAQ

What is Reaction at Fulcrum Pin of Rocker Arm?

The Reaction at fulcrum pin of rocker arm is the reaction force acting onto the fulcrum pin ( the pivot about which a lever turns) used as a joint at a fulcrum point, as a result of force due to exhaust valve reaction and force on the roller pin and is represented as R_f = sqrt(P_e^2+P_c^2-2*P_c*P_e*cos(θ)) or 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)). 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 & Angle Between Rocker Arms is the angle between the two arms of a rocker arm or the contained angle between the rocker arms.

How to calculate Reaction at Fulcrum Pin of Rocker Arm?

The Reaction at fulcrum pin of rocker arm is the reaction force acting onto the fulcrum pin ( the pivot about which a lever turns) used as a joint at a fulcrum point, as a result of force due to exhaust valve reaction and force on the roller pin is calculated using 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)). To calculate Reaction at Fulcrum Pin of Rocker Arm, you need Total Force on Rocker Arm of Exhaust Valve (P_e), Force on Roller Pin (P_c) & Angle Between Rocker Arms (θ). With our tool, you need to enter the respective value for Total Force on Rocker Arm of Exhaust Valve, Force on Roller Pin & Angle Between Rocker Arms and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.

How many ways are there to calculate Force at Fulcrum Pin?

In this formula, Force at Fulcrum Pin uses Total Force on Rocker Arm of Exhaust Valve, Force on Roller Pin & Angle Between Rocker Arms. We can use 3 other way(s) to calculate the same, which is/are as follows -

Force at Fulcrum Pin = Total Force on Rocker Arm of Exhaust Valve*sqrt(2*(1-cos(Angle Between Rocker Arms)))
Force at Fulcrum Pin = Diameter of Fulcrum Pin*Length of Fulcrum Pin*Bearing Pressure for Fulcrum Pin
Force at Fulcrum Pin = (Shear Stress in Fulcrum Pin*pi*Diameter of Fulcrum Pin^2)/2

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