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What is a Degree of Freedom?
Table of Contents:
We have learned about Truss and how it is a combination of multiple rods or bars joined together to form a rigid structure. The rigidity of a structure is important. And to do so the joints between the two members should be strong. But what are these joints? Let's take a look.
When two or more surfaces are joined together by means of permanent or temporary linking, forms a joint.
Just like the joints in our body, there are mechanical joints.
A joint between two or more members can possibly restrain or limit the degree of freedom of the mechanism or component. This depends on the type of joint employed and the characteristic features of the mechanism.
What is the Degree-of-Freedom (DoF) of an object?
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Any mechanical system has a number of parameters that define its state or configuration. Those parameters are defined by Degree-of-Freedom of that object. It is important in the analysis of a system of bodies or a structure.
There are in total, six degrees of freedom.
Degree of freedom can be described as the constraints on a body to restrict free movement along a direction.
To calculate the degree of freedom of a component we use the below equation:
DOF = 6 x (number of bodies not including ground) – constraints
where constraints are the number of restricted motions on the body.
Let's look at an example to understand it clearly i.e. A door is fixed using two pin joints (hinges).
The door is the singular body here. Hence, the number of bodies not including ground is 1.
The pin joint or the hinges are able to rotate along its axis. i.e. the door rotates about its axis and is not able to move in the remaining 5 directions. Therefore the constraints are 5.
DOF = 6 x (1) - (5) = 1
The degree of freedom is 1.
What does the degree of freedom have to do with joints though? Well, the joint used in the object will affect the maximum degree of freedom of the body. Along with the degree of freedom, we have to look out for another term - kinematic pair.
Kinematic pair
A kinematic pair is a connection between two physical objects that imposes constraints on their relative movement.
Let us now take a look at the types of joints.
There are different types of joints.
Pin joint - A pin joint is a linkage between two components achieved by passing a pin through the cylindrical cavity of the two connecting objects. The central axis is common and the objects are constrained to pure rotation along that axis. The degree of freedom here is one.
Prismatic joint - A joint which provides linear sliding motion between two bodies, also known as a slider is a prismatic joint. The degree of freedom here is one.
Ball joint - A joint which constitutes a ball bearing and a socket is a ball joint. The degree of freedom here is three.
Knuckle joint - A knuckle joint is used to connect two rods that are under tensile load. This joint is formed using three components, Single eye, Double eye or fork, and Knuckle pin. The degree of freedom here is one.
Turnbuckle - Most commonly scene in ropes or cables, where two ropes on tension are joined by a screw-like mechanism on both connecting ends.
Cotter joint - Similar to the pin joint, a cotter joint has a pin passing through a common cavity. Mostly found in cranks or pedals, this joint has a freely rotating grip/arm.
Bolted joint - Also known as fasteners, bolted joints are as the name suggests are joints made by means of a bolt and nut combination to hold two components of the mechanism together.
Screw joint - Screw joints are used readily for temporary and faster connection of two components. With a screw joint, it is easier to undo the joint. The degree of freedom here is one.
Universal joint - A joint comprised of coupling and rods connected with their axis at an angle. The degree of freedom here is one. The shafts/rods are able to rotate along their axes.
Just like in human body, two bones are joint, in mechanical system we have joints to join two components of a machine.
Various joints provide the functionality of power transmission. The ratio at which the power is delivered depends on the type of join employed. A simple moving automobile can have up to 10000 joints.
Summary:
Any moving mechanism has a degree of freedom and each component of that mechanism has its individual degree of freedom.
A joint is also capable of power transmission.
Kinematic pair between two components defines the constraints on the movement of the paired object. The relative motion of the object is restricted.
Most mechanical joints allow relative movement and have one degree of freedom.
A lower pair is an ideal joint that constrains contact between a surface in the moving body to a corresponding surface in the fixed body.
Mechanisms, manipulators, or robots are typically composed of links connected together by joints.
We have learned about the different types of joints and their properties. The joints we studied so far were temporary and allowed the motion. In mechanical structures, we have permanent joints as well. Such as welded joints and riveted joints. To know more about these types of joints, stay tuned to our blog.
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