Kinematics: Types of joints continued

First Order Pin Joints: This type of joints have two or more Links and are said to be of Order One less than the Number of Links joined. 

In the above Fig. you can notice there are two links joined by a pin, therefore, the Order of the joint is First. The Degree of Freedom i.e. DOF = One 

Second Order Pin Joint: In this type of joint there are there links joined by a pin. Since the number of Links is three the Order (of the joint will be one less than three) is said to be Second Order. 

In the Fig., posted above, you can see if Link L1 is taken as the reference Link then the other two Links L2 and L3 will rotate, (with respect to L1 as shown in the Fig.) the Degree of Freedom i.e. DOF = Two

A Roller on A Plane: This is an example of Higher pair. The pair is entirely different type of pair (joint). You can see in the Fig. posted below, that the Roller is simply placed on a plane without being joined by a pin or a slot, but is in contact with the plane. 

There are three kinds of possible motions in such joints (pairs), the Roller can simply Roll Or can Slide Or can Roll and Slide, over the plane depending on the friction between roller and the plane. The DOF is either One or Two. When the Roller only rolls the DOF = 1, when it only slides DOF = 1 and when it rolls and slide at the same time the DOF = 2.

Kinematic Joints: Types explained with images

Rotating full Pin type Joint: In the Fig. posted below there are two Links joined by a pin. The links can have only rotational movement with respect to each other. In this type of joint the Degree of Freedom  is one. This is a Lower pair. 

Translating Slider: You can see in the Fig. posted below that the Slider can move only inside the slot, along the 'x' axis .This type of joints are known as Translating full slider. This type of joint falls under the category of a lower pair. The joint has one Degree of freedom. 

Link against Plane: This type of joint falls under the higher pair category. This is an example of  a joint which has Two degrees of Freedom. By looking at the diagram one can understand that it can move along 'x' Axis and rotate too. 

Pin in Slot: In the diagram, posted below,you can see that the link is connected to the slot by means of a pin. It is evident that the slot will permit movement along 'x' Axis, the link is free to rotate also. The joint, therefore, has Two Degrees of Freedom.It falls under the higher pair category.

Types of Joints - Pictorial views: Their Degrees of Freedom

1. Rotational Type: The Fig. posted below shows the pictorial representation of a Rotational Joint. This joint has only One degree of Freedom. As you can see from the Fig. posted, the joint permits only rotational motion, shown by the arrow. It is constrained in the Axial-Directions. 

2. Sliding Type: The Fig., posted below, shows the pictorial representation of a Sliding joint. This joint has only One Degree of Freedom.You can see, the movement in just one direction is permitted. The arrows indicates that the inner square can move only axially, along - X-axis

3. Helical Type: The Fig.,posted below, shows the pictorial view of the Helical joint.  You may notice that the Screw is permitted to rotate. Although it moves in the linear direction, when it rotates, but it is not possible to push it axially. Therefore, it is said to possess only One degree of Freedom, shown by the arrow.

4. Cylindrical Type: The Fig., posted below, shows pictorial representation of a Cylindrical Joint. You can see that in this type of joint the shaft can rotate and slide along its center line too, as indicated by the arrows. It is, therefore, said to have Two Degrees of Freedom.

5. Spherical Type: The Fig., posted below is the pictorial representation  of the Spherical Joint. This is also known as a Ball & Socket joint. You may see that the pin connected to the ball can rotate around all the 3 - Axes i.e. 'X',  'Y' and  'Z'. Therefore, we call it a joint with Three Degrees of Freedom. 

6. Planar Type: The Fig., posted below, shows the pictorial representation of a Planar type joint  You may have noticed, in this case the block is free to slide along the 'X' and 'Y' Axes and also rotate around Z Axis, shown by the arrows. That is why this type also is said to have Three Degrees of Freedom.  

Kinematic Chains: Inversions --- Part 3

The Third Inversion more examples:

One of the most interesting application of Third-Inversion is the Rotary-Engine of an Air-Craft, shown in the Fig. posted below;

In case of the Rotary-Engines, the crank, item -2 in the fig, is fixed to the frame ----- and the propeller was attached to the rotating  crank-case. Now a days the use of rotary-engines has drastically reduced owing to the advent of Jet-Engines ---- which are faster, have better fuel economy and are more reliable. You may be aware this type of engines were extensively used in World-War- I.

Fourth-Inversion: 

In the Fourth-Inversion the slider is fixed, as shown is the diagram posted below;

The very commonly used application of fourth inversion is a Hand-Operated Pump, shown below;

Kinematic Chains: Inversions - Part-2

3. Inversion - Third type: 

The Third-Inversion is done by fixing the Crank- as shown in the Fig. below. This is an inversion of Slider-Crank mechanism, you may recall, was discussed while discussing  Grashof-type-Chains.

This is the inversion on which Whitworth-Quick-Return-Mechanism is based on.The Whitworth-mechanism is widely used in Shaping-Machines. In this inversion the Link-3, of the Fig. below, is the Driver which rotates at a uniform angular velocity. and makes the Rocker oscillate.  The point 'D' of the Rocker is connected to the Ram with the help of Link-5. As the Rocker moves back and forth it moves the slider back and forth too.