Kinematic chains, mechanisms, machines, link classificatio

Kinematic chains:-

• Kinematic chain: links joined together for motion

• Mechanism: grounded kinematic chain

• Machine: mechanism designed to do work

Link classification:-

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.


Elements:

 

0: Ground (Casing, Frame)

1: Rocker

2: Coupler

3: Crank

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

Where:

L: number of links

J: number of full joints

G: number of grounded links.

Determining DOF’s

• Gruebler’s equation for planar mechanisms    M= 3L-2J-3G

• Where

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

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