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 • the degree-of a joint is the number of links

connected at the oint minus one.

Binary Joint Ternary Joint Quarternary Joint

!!!! Do not confuse with the degree of freedom of a joint

Note that the number of joints at that connection is equal to the.

Degree of freedom of a joint is the number of independent

parameters required to define the position of one link relative to the

other connected by that joint.

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  echanisms

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  echanisms

Degree of freedom of a

mec an sm

is the number of independent

the position of every link in that

mechanism.

Readin Assi nment: u to a e 33 End of Cha ter 1 b October 13 ‘08

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C

 b

B c

a

A D

θ

d 

B

 b

C

θ

a

φ

ED

e

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 • De ends on:

 – The degree of freedom of space

 –

 – The number of links and joints in the

mechanism – The distribution of links and joints within the

mechanism

Does not de end onThe shape of the links

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Let

  = Degree-of-freedom of space:= 3 for planar and spherical space

  = 6 for spatial space

  = Number of links in a mechanism (including the fixed link).

 j = Number of joints in the mechanism

f = Degree-of-freedom of the ith joint

F = Degree-of- freedom of the mechanism

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Consider four links in plane motion

For 4 links 4*3=12 parameters are needed

For   links (with one link fixed):

 (  -ı) parameters are required. This is the number of parameters needed without joints (constraints)

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With the oints shown: 

Link 2 3Parameters

Link 3 2 Parameters (Cylinder in slot joint has 2 Dof, constrains 1 Dof in plane motion).

n arame er revo u e o n s as o , cons ra ns o n ane mo on

Link5 1 Parameter (revolute Joints has 1 Dof, constrains 2 Dof in Plane motion)

With these 3 joints 1+2+2 = 5 freedoms are constrained

 j j

Therefore now we need (12-5) 7 parameters to determine the position of these 4 links

If the joint freedom is f i, then that joint constrains   – f i freedoms. j joints will constrain:

∑ ∑= =

−=−i i

ii   f  j f 1 1

)(   λ λ  freedoms

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  ,

. .

 j

F j f ii

= − − −=

∑λ λ( ) ( ) 11

or  j

i

i

= − − +=1

General Degree-of-freedom equation

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- -

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Schematic Drawing

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Virtual Model

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6

4

2

3

10

9

8

7

1

12  13

Inverted Slider-Crank Mechanism

Drawn by: Eres SöylemezChecked b : Eres Sö lemez

5

 

Date September 15 2004METU

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Example

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Example: Excavator 

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-

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Hinge

1972

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Example:

  .The mechanism shown is an adjustable stroke pump. The mechanism is driven by an electric

motor attached to the input crank to impart a translating motion to the piston. The adjustment

on the amount of stroke of the um is made b a screw not shown which chan es the

 position of the pin A.

5

1C

s

P

3

Cs

2RR

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Example

Three Gear Drive

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Example

Landing Gear door with controlled Kinematic Control

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Example

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  echanisms

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Example

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Example

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Linked Multi-Segment Landing Gear Door for Aircraft

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Example:

Some spatial mechanisms

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