Degrees of Freedom
Often we hear this word "Degree of Freedom" in Kinematics, Engineering Mechanical and so on. Many of them had confusing with this topic. Now I am going to tell about this.
Degrees of Freedom – Number of independent coordinates required to completely specify the position of the link.
We know that there are two types of motion
i) Linear motion,
(1) Movement along X- axis
(2) Movement along Y-axis
(3) Movement along Z-axis
ii) Rotational motion
(1) Rotation about X- axis
(2) Rotation about Y-axis
(3) Rotation about Z-axis
Now combine these all, we get six motions.
Grubler Condition
Any link in a plane has 3 DOF. Therefore, a system of L unconnected links in the same plane will have 3L DOF. When these links are connected by a full joint this removes two DOF, and when these links are connected to half joint it removes only one DOF from the system (because a half joint has two DOF). In addition, when any link is grounded or attached to the reference frame, all three of its DOF will be removed.
Grubler Equation
M=3L-2J-3G
where:
M = degree of freedom or mobility
L = number of links
J = number of joints
G = number of grounded links
M=3(L-1)-2J
Kutzbach’s Modification of Grubler’s Equation
Kutzbach’s Modification of Grubler’s Equation is:
M=3(L-1)-2J1-J2
where:
M = degree of freedom or mobility
L = number of links
J1 = number of 1 DOF (full) joints
J2 = number of 2 DOF (half) joints
If DOF ≤ 0 then it will be a structure.
If DOF > 0 then it will be a mechanism.
The value of J1 and J2 in these equations must still be carefully determined to account for all full, half, and multiple joints in any linkage. Multiple joints count as one less than the number of links joined at that joint and add to the "full" (J1) category.
Lets see some examples:
1. An Aeroplane has 6 six degree of freedom.
2. A Camera has also Six degree of freedom while it is placed in its stand.
