Length of Fulcrum Pin of Rocker Arm given Reaction at Pin Calculator

✖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%
✖Shear Stress in Fulcrum Pin is the shear stress induced into the pin, the force per unit area tending to cause deformation of the pin by slippage along a plane parallel to the imposed stress.ⓘ Shear Stress in Fulcrum Pin [τ_fulcrum]			+10% -10%

✖Length of Fulcrum Pin is the total length of the pin used at the fulcrum joint.ⓘ Length of Fulcrum Pin of Rocker Arm given Reaction at Pin [l₁]

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Formula

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Length of Fulcrum Pin of Rocker Arm given Reaction at Pin

Formula

`"l"_{"1"} = 1.25*sqrt((2*"R"_{"f"})/(pi*"τ"_{"fulcrum"}))`

Example

`"31.10531mm"=1.25*sqrt((2*"3560N")/(pi*"3.66N/mm²"))`

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Length of Fulcrum Pin of Rocker Arm given Reaction at Pin Solution

STEP 0: Pre-Calculation Summary

Formula Used

Length of Fulcrum Pin = 1.25*sqrt((2*Force at Fulcrum Pin)/(pi*Shear Stress in Fulcrum Pin))
l₁ = 1.25*sqrt((2*R_f)/(pi*τ_fulcrum))
This formula uses 1 Constants, 1 Functions, 3 Variables

Constants Used

pi - Archimedes' constant Value Taken As 3.14159265358979323846264338327950288

Functions Used

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

Length of Fulcrum Pin - (Measured in Meter) - Length of Fulcrum Pin is the total length of the pin used at the fulcrum 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.
Shear Stress in Fulcrum Pin - (Measured in Pascal) - Shear Stress in Fulcrum Pin is the shear stress induced into the pin, the force per unit area tending to cause deformation of the pin by slippage along a plane parallel to the imposed stress.

STEP 1: Convert Input(s) to Base Unit

Force at Fulcrum Pin: 3560 Newton --> 3560 Newton No Conversion Required
Shear Stress in Fulcrum Pin: 3.66 Newton per Square Millimeter --> 3660000 Pascal (Check conversion here)

STEP 2: Evaluate Formula

Substituting Input Values in Formula

l₁ = 1.25*sqrt((2*R_f)/(pi*τ_fulcrum)) --> 1.25*sqrt((2*3560)/(pi*3660000))

Evaluating ... ...

l₁ = 0.0311053097737149

STEP 3: Convert Result to Output's Unit

0.0311053097737149 Meter -->31.1053097737149 Millimeter (Check conversion here)

FINAL ANSWER

31.1053097737149 ≈ 31.10531 Millimeter <-- Length of Fulcrum Pin

(Calculation completed in 00.004 seconds)

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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

Length of Fulcrum Pin of Rocker Arm given Reaction at Pin Formula

Length of Fulcrum Pin = 1.25*sqrt((2*Force at Fulcrum Pin)/(pi*Shear Stress in Fulcrum Pin))
l₁ = 1.25*sqrt((2*R_f)/(pi*τ_fulcrum))

Forces acting on the 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 Length of Fulcrum Pin of Rocker Arm given Reaction at Pin?

Length of Fulcrum Pin of Rocker Arm given Reaction at Pin calculator uses Length of Fulcrum Pin = 1.25*sqrt((2*Force at Fulcrum Pin)/(pi*Shear Stress in Fulcrum Pin)) to calculate the Length of Fulcrum Pin, The Length of Fulcrum Pin of Rocker Arm given Reaction at Pin is the total length of the fulcrum pin used at the fulcrum joint of the two rocker arms. Length of Fulcrum Pin is denoted by l₁ symbol.

How to calculate Length of Fulcrum Pin of Rocker Arm given Reaction at Pin using this online calculator? To use this online calculator for Length of Fulcrum Pin of Rocker Arm given Reaction at Pin, enter Force at Fulcrum Pin (R_f) & Shear Stress in Fulcrum Pin (τ_fulcrum) and hit the calculate button. Here is how the Length of Fulcrum Pin of Rocker Arm given Reaction at Pin calculation can be explained with given input values -> 31105.31 = 1.25*sqrt((2*3560)/(pi*3660000)).

FAQ

What is Length of Fulcrum Pin of Rocker Arm given Reaction at Pin?

The Length of Fulcrum Pin of Rocker Arm given Reaction at Pin is the total length of the fulcrum pin used at the fulcrum joint of the two rocker arms and is represented as l₁ = 1.25*sqrt((2*R_f)/(pi*τ_fulcrum)) or Length of Fulcrum Pin = 1.25*sqrt((2*Force at Fulcrum Pin)/(pi*Shear Stress in 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 & Shear Stress in Fulcrum Pin is the shear stress induced into the pin, the force per unit area tending to cause deformation of the pin by slippage along a plane parallel to the imposed stress.

How to calculate Length of Fulcrum Pin of Rocker Arm given Reaction at Pin?

The Length of Fulcrum Pin of Rocker Arm given Reaction at Pin is the total length of the fulcrum pin used at the fulcrum joint of the two rocker arms is calculated using Length of Fulcrum Pin = 1.25*sqrt((2*Force at Fulcrum Pin)/(pi*Shear Stress in Fulcrum Pin)). To calculate Length of Fulcrum Pin of Rocker Arm given Reaction at Pin, you need Force at Fulcrum Pin (R_f) & Shear Stress in Fulcrum Pin (τ_fulcrum). With our tool, you need to enter the respective value for Force at Fulcrum Pin & Shear Stress in Fulcrum Pin 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 Length of Fulcrum Pin?

In this formula, Length of Fulcrum Pin uses Force at Fulcrum Pin & Shear Stress in Fulcrum Pin. We can use 3 other way(s) to calculate the same, which is/are as follows -

Length of Fulcrum Pin = Force at Fulcrum Pin/(Diameter of Fulcrum Pin*Bearing Pressure for Fulcrum Pin)
Length of Fulcrum Pin = Diameter of Fulcrum Pin*1.25
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))

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