DME-III_Design of Machine Elements_Knuckle Joint

Knuckle Joint Design Procedure

       Before going into detailed steps to design the dimensions of the Knuckle joint, it is essential to get oriented with all its components and their functions. Here is the diagram showing the exploded view  of Knuckle Joint.

As seen in the assembly the Knuckle joint has main four parts

1. Rods {Which are to be connected by joint }
2. Single eye {Modified rod for assembly}
3. Double eye or Forked end {Modified rod for assembly}
4. Pin {Connects the two rods}
5. Collar {to keep the pin in position}
6. Split pin or taper pin {Not in diagram} {to prevent sliding away of pin}

Assembly Drawing and Notations used in Knuckle Joint

Notations used in design :

P  =  Tension in rod ( Load on the joint)

D =  Diameter of rod

D₁= Enlarged diameter of rod

d = Diameter of pin

d₁ = Diameter of pin head

d₀ = Outer diameter of eye or fork

t1 = thickness of eye end 

t2= thickness of forked end (double eye)

x= distance of the Centre of fork radius R from the eye 

STEPS TO DESIGN KNUCKLE JOINT 

• Step 1 : Design of Rods (D,D₁)

Tensile failure of rod 

Using basic strength equation

Load = Stress * Area
P=Area Resisting Tension * Allowable tensile stress

        From This equation Diameter ‘D’ of rod can be found

Empirical relations

Using Empirical relations the enlarged diameter of rod D₁ is determined

     D₁=1.1*D

• Step 2 : Decide the thickness of eye end and forked end (t₁,t₂)

Empirical relations

Both these dimensions are decided on the basis of empirical relations,

t₁= 1.25 D    and    t₂= 0.75 D

• Step 3 : Decide the dimensions of pin (d,d₁)

Double shear Failure

The pin may get sheared off into three pieces as shown below, since the pin breaks at two places it is called double shear. Both areas are taken as resisting areas.

Using basic strength equation

Load = Stress * Area

P=(Area Resisting Shear)*(Allowable Shear Stress)       

                   

     Note that 2 is because of double shear ...From This equation Diameter ‘d’ of pin can be found. But since the pin is also subjected to bending one more diameter of pin on the basis of bending is determined and the bigger of both is taken as the final size of pin.

Bending failure of pin

The diameter on the basis of bending is determined using the following formula,

 Calculate d from this formula

Empirical relation for pin head diameter

Since pin head is not subjected to any stress, its diameter is simply decided on the basis of proportionality, (it is taken 50% more than that of pin diameter )

                  d₁=1.5 d

• Step 4 : Check Stresses in Eye end 

Empirical relation for outside diameter of eye and fork

                  

                         d₀=2d

Tensile failure of eye end

               The single eye may fail in tension as shown below { please note that when the plane of failure is perpendicular to the direction of force then the failure is either tensile or compressive}

Using the basic equation for stress

P=(Area Resisting tension)*(Allowable tensile Stress) 

          Using this equation find the value of sigma t  and check if it is less than allowable value for design to be safe.

{Note that area resisting the tension is rectangular one and not circular so its area is length time height total length is (d0-d) and height is t1.

Shear failure of eye end

    The single eye may fail in shear as shown below { please note that when the plane of failure is parallel to the direction of force then the failure is Shear failure}

Using the basic equation for stress

P=(Area Resisting Shear)*(Allowable Shear Stress)  

  ..................simplifying this equation we get 

  

 .......Using this equation find the value of   and check if it is less than allowable value for design to be safe.

Crushing Failure of eye end

     The single eye is also subjected to Crushing between pin and inner face of single eye. In case of crushing failure since the area is curved we take the projected (area which would be visible in drawing) of the cylindrical area. As we know that a cylinder appears as a rectangle in projection, hence the area will be diameter times the height of cylinder. This area is illustrated below,

         

Using the basic equation for stress

P=(Bearing Area Resisting )*(Allowable Stress) 

 ………….Using this equation find the value of  and check if it is less than allowable value for design to be safe.

• Step 5 : Check Stresses fork end

Fork end is also subjected to same failures as that of eye end, the only difference is that it has two eyes. So we get the same equations except multiplied by 2.

The equations for tensile, shear and crushing failures are given below

Tensile failure of  fork end

   {see the changes highlighted in red from the equation of single eye} Get the value of induced tensile stress from this equation and confirm that it is below allowable tensile stress.

Shear failure of  fork end

 {see the changes highlighted in red from the equation of single eye} Get the value of induced shear stress from this equation and confirm that it is below allowable shear stress.

Crushing failure of  fork end

 {see the changes highlighted in red from the equation of single eye}  Get the value of induced crushing stress from this equation and confirm that it is below allowable crushing stress.

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