# Mechanical joint

A mechanical joint is a section of a machine which is used to connect one or more mechanical part to another. Mechanical joints may be temporary or permanent, most types are designed to be disassembled. Most mechanical joints are designed to allow relative movement of these mechanical parts of the machine in one degree of freedom, and restrict movement in one or more others. Mechanical joints are much cheaper and are usually bought ready assembled.[1]

## Knuckle joint

A knuckle joint is used to connect the two rods which are under the tensile load when there is requirement of a small amount of flexibility or when angular movement is necessary. There is always axial or linear line of action of load.

The knuckle joint assembly consists of the following major components:

1. Single eye.
2. Double eye or fork
3. Knuckle pin.

At one end of the rod the a single eye is formed and a double eye is formed at the other end of the rod. Both, single and double eye are connected by a pin inserted through the eye. The pin has a head at one end and at other end there is a taper pin or split pin. For gripping purpose, the ends of the rod are of octagonal forms. Now, when the two eyes are pulled apart, the pin holds them together. The solid rod portion of the joint in this case is much stronger than the portion through which the pin passes.[2]

The modes of failure are:

1. Shear failure of pin (single shear).
2. Crushing of pin against rod.
3. Tensile failure of flat end bar.

Application:

1. Tie rod joint of roof truss.
2. Tension link in bridge structure.
4. Tie rod joint of jib crane.
5. The knuckle joint is also used in tractor.[3]

### Design of knuckle joint

ref: [2]

The assembly diagram of knuckle joint is as shown in fig.

The dimension of knuckle joints are:

• Diameter of rod = d
• Diameter of knuckle pin = dp
• Outside diameter of single eye = doe
• Outside diameter of double eye = dod
• Thickness of single eye = t
• Thickness of fork = t1
• Axial tensile force on rod = P

(1) Diameter of rod

Consider the rod is subjected to a direct tensile stress

```    ς = P / π d2
```

From above equation, diameter of rod 'd' is obtained.

(2) Design of pin (dp)

(a) Consider the failure of pin under double shear due to tensile force.

Therefore, direct shear stress induced in knuckle pin is given by Equation

```    ς = P / 2A = (P/2) / (π/4) dp2 = 2P / π dp2
```

(b) Failure of knuckle pin in bending

Assume there is no clearance or slack but in actual, knuckle pin is loose in forks to permit angular moment of one with respect to other, so it is subjected to bending moment in addition to shear, consider uniformly distributed load along the portion of pin.

```    M = [(-P/2) × (t/4)] + { (P/2) × [ (t/2)+(t1/3) ] }
= P/2 [(t1/3)+(t/2)-(t/4) ]
= P/2 [ (t1/3)+(t/4) ]
```

Section modulus,

```    Z = (π/ 32)dp3
```

Maximum bending stress, σb

```    σb= M/Z = { P/2 [(t1/3)+(t/4)] } / {(π/ 32)dp3}
```

Here,we check the pin in bending and find the value of dp

(3) Design of single eye :

(a) To find the outside diameter of single eye (doe) The single eye is subjected to a direct tensile stress, due to this single eye under tear.

```    σt = P/A = P/ (doe-dp)× t
```

(b) Due to direct tensile strength, the single eye is subjected to double shear.

```    Resisting shearing area = 2(doe-dp)×(t/2)
```

The direct shear stress induced is

```    ς=P/(doe-dp)×t
```

From this equation the outside diameter of single eye doe is obtained.

(C) Failure of single eye or pin due to tensile load in crushing

```    Resisting crushing area = dp × t
σc = P/(dp×t)
```

Form this equation crushing stress checked if fail, increase the thickness of eye (t).

(4) Design of fork (double eye):

(a) The tearing of the double eye at weakest section due to tension

```    Area resisting tear = (dof – dp) × 2 t1
σt =    p/ [(dof – dp) × 2 t1]
```

From this equation, find the outside diameter of fork (dof).

(b) Failure of double eye (fork) in double shear due to tensile load.

```    Area resisting shear  = 4 × [(dof – dp) ]/2 × t1
= 2 × (dof – dp) t1
```

The shear stress is given by,

```    ς = p/[(dof – dp) × 2 t1]
```

From this equation, check shear stress if less than design, increase thickness of fork t1.

(c) Failure double eye in crushing (thickness of fork)

Double eye may fail in crushing due to tensile load

The crushing stress is given by,

```    σc = P/( 2×dp ×t1)
```

Check crushing stress or find t1

## Turnbuckle

The buckle or a coupler is a mechanical joint used to connect two members which are subjected to tensile loading which require slight adjustment of length or tension under loaded conditions. It consists of central hexagonal nut called coupler and tie rod having right-hand and left-hand threads. A coupler of hexagonal shape is to facilitate the turning of it with a spanner or sometime a hole is provided in the nut so that a tommy bar can be inserted for rotating it. As the coupler rotates, the tie rods are either pulled together or pushed apart depending upon the direction of the rotation coupler. Normally the tie rods are made of steel, while the coupler is made of steel or C.I.

Application :

1. To tighten the members of the roof truss.
2. Used to connect link in a mechanism to transfer motion
3. Used between the two railway wagon or bogies.
4. To tighten the cable or stay ropes of electric distribution poles.

### Design of turnbuckle

Consider a turnbuckle, subjected to an axial tensile force P. The various dimensions of the turnbuckle are calculated as follows:

(1) Diameter of tie rod ‘dc2 :

Due to axial tensile load p, the rod is subjected to tensile stress. Also due to twisting moment in the tie rod.

The tie rod is design for direct tensile load of Pd=1.25P

The tensile stress induced in tie rod is given by

```    σt = 4Pd/ (π×dc×dc)
```

From above equation the core diameter of the tie rod is obtained. The nominal diameter can be selected from I.S.O metric screw threads table or it can be found by,

```    do = dc/ 0.84
```

(2) Length of couple nut (ln) :

Consider the direct shearing of the thread at the root of the coupler nut and the screw.

(a) The direct shear stress induced in screw thread is

```    ςs =  P/(π×dc×ln)
```

(b) The direct shear stress induced in nut

```    ςn =  P/ (π×do×ln)
```

Where,

```    ςs and ςn  = shear stress in screw and nut respectively in N/mm2
do  =   Nominal diameter of the screw
dc =  Core diameter of the screw
ln =  Length of the coupler nut
```

(c) Check of crushing of the thread

```    crushing resistance of the thread = (π/4) × [do2- dc2] ×n×ln× σc
Where, n  =   number of threads per length  = ln/p
σc = crushing stress induced in the coupler
p = pitch of the thread in mm
```

Equating the design load with crushing resistance

```    pd  = (π/4) × [do2- dc2] ×n×ln× σc
```

(3) Outside diameter of the coupler nut (D) :

The coupler nut is subjected to a direct tensile load P and a torque T.

Consider tearing of the coupler nut due to tensile stress induced in it. In order to account for the torque, the tensile load is taken as Pd.

The tensile stress induced in coupler nut is given by

```    σt = 4P/(π×(D2- do2))
```

By empirical relation, the outside diameter of the coupler nut D is taken as

```    D = 1.25 do or 1.5 do
```

(4) Outside diameter of coupler (D2):

```    Let,D1= Inside diameter of the coupler
D2 = Outside diameter of the coupler
```

Consider a coupler is subjected to direct tensile load P and a torque T. So for design the coupler outside diameter, the design load is considered.

By empirical relation,

The outside diameter of the coupler D2 is taken as,

```    D2 = 1.5do or 1.75 do
```

(5) Length of the coupler nut (Ln)

```    Ln  = 6 do
```

(6) Thickness of the coupler

```    Coupler_Thickness = t = 0.75 do
```

(7)Thickness of the coupler nut

```    Coupler_nut_Thickness = t1 = 0.5 do
```

## Cotter joint

This is used to connect rigidly two rods which transmit motion in the axial direction, without rotation. These joints may be subjected to tensile or compressive forces along the axes of the rods. The very famous example is the joining of piston rod's extension with the connecting rod in the cross head assembly.

• Quick assembly and disassembly is possible
• It can take tensile as well as compressive force.

Application:

• Joint between piston rod and cross head of a steam engine
• Joint between valve rod and its steam
• A steam engine connecting rod strap end
• Foundation bolt

## References

1. ^ Blake, Alexander (1985). Design of mechanical joints. CRC Press. ISBN 978-0-8247-7351-9.
2. ^ a b Gupta, R.S. Khurmi, J.K. (2008). A textbook of machine design (S.I. units) : [a textbook for the students of B.E. / B.Tech., U.P.S.C. (Engg. Services); Section 'B' of A.M.I.E. (1)] (14th ed.). Ram Nagar, New Delhi: Eurasia Publishing House. ISBN 81-219-2537-1.
3. ^ Bhandari, V.B. (2001). Introduction to machine design. New Delhi: Tata McGraw-Hill. ISBN 978-0-07-043449-3.
4. ^ https://www.scribd.com/doc/27822626/Design-of-Turnbuckle. "Design-of-Turnbuckle". Missing or empty `|url=` (help); `|access-date=` requires `|url=` (help)