• Kinematic chain: links joined together for motion
• Mechanism: grounded kinematic chain
• Machine: mechanism designed to do work
Ground: any link or links that are fixed, nonmoving with respect to the reference frame
Crank: pivoted to ground, makes complete revolutions
Rocker: pivoted to ground, has oscillatory motion
Coupler: link has complex motion, not attached to the ground.
0: Ground (Casing, Frame)
The “Ground” Link:-
When studying mechanisms it is very helpful to establish a fixed reference frame by assigning one of the links as “ground”.
The motion of all other links are described with respect to the ground link.
For example, a fourbar mechanism often looks like a 3-bar mechanism, where the first “bar” is simply the ground link.
Determining Degrees of Freedom
Two unconnected links: 6 DOF (each link has 3 DOF)
When connected by a full joint: 4 DOF (each full joint eliminates 2 DOF)
Gruebler’s equation for planar mechanisms: DOF = 3L-2J-3G
L: number of links
J: number of full joints
G: number of grounded links.
• Gruebler’s equation for planar mechanisms M= 3L-2J-3G
M = degree of freedom or mobility
L = number of links
J = number of full joints (half joints count as 0.5)
G = number of grounded links =1
M = 3(L-1) – 2J
Kutzbach¡¦s modification of Gruebler¡¦s equation