Degrees of freedom
The connection of a link with another imposes certain constraints on their relative motion thus,
Degrees of freedom = 6 – number of restraints
Degree of Freedom of Space Mechanism (3-D)
F = 6(L – 1) – 5P1 – 4P2 – 3P3 – 2P4 – P5
Here, F = Degree of freedom (D.O.F.)
L = Total number of links in mechanism
P1 = Number of pairs having one D.O.F.
P2 = Number of pairs having two D.O.F.
P3 = Number of pairs having three D.O.F.
P4 = Number of pairs having four D.O.F.
P5 = Number of pairs having five D.O.F.
- Degree of freedom of plane (2D) mechanism (Gruebler’s Criterion)
F = 3(L– 1) – 2P1 – P2
Here, L = Number of links in a mechanism
P1 = Number of pairs having one degree of freedom
P2 = Number of pairs having two degree of freedom
- Kutzback’s equation
F = 3(L – 1) – 2j – h
Here, L = Number of link, j = Number of lower joints,
h = Number of higher joints
- Grubler’s Equation: For those mechanisms which have single degree of freedom and zero higher pair.
3l – 2j – 4 = 0
Here, l = Number of links, j = Number of binary joints
- Degree of Freedom: F = 0 (Frame), F < 0 (Redundant frame)
F > 0 (constrained/unconstrained frame)
All mechanisms have minimum 4 number of links.
<< Previous | Next >>
Must Read: What is the Theory of Machines?
Dear Aspirants,
Your preparation for GATE, ESE, PSUs, and AE/JE is now smarter than ever — thanks to the MADE EASY YouTube channel.
This is not just a channel, but a complete strategy for success, where you get toppers strategies, PYQ–GTQ discussions, current affairs updates, and important job-related information, all delivered by the country’s best teachers and industry experts.
If you also want to stay one step ahead in the race to success, subscribe to MADE EASY on YouTube and stay connected with us on social media.
MADE EASY — where preparation happens with confidence.
MADE EASY is a well-organized institute, complete in all aspects, and provides quality guidance for both written and personality tests. MADE EASY has produced top-ranked students in ESE, GATE, and various public sector exams. The publishing team regularly writes exam-related blogs based on conversations with the faculty, helping students prepare effectively for their exams.
