Calculate mobility of the linkages shown below SolutionSol P

Calculate mobility of the linkages shown below.

Solution

Sol: (Please check your picture and try to post it in correct orientation in future)

Inorder to calculate the mobility i.e the Degree of freedom.

We use the Gruebler\'s equation for linkages which is given as:

D.O.F=3(n-1)-2l-h

where: n= number of linkages(which includes individual,plate and the frame itself)

l= number of lower pairs (which includes slider i.e prismatic pair and hinge joint i.e a rotating pair)

Also, lower pairs will form a surface contact causing it to move in only 1 direction) . The remaing 2 direction are fixed, Hence.\"2*l\" in the equation.

h= number of higher pair( which includes a ball-socket joint usually identified as a line contact pair i.e it will have a line contact thorughout its motion).

2.1)

The first figure compires of a fixed plane noted \"1\" as well as the far end point which is fixed,\" 2-6\", as linkages including plate and singlular linkages.

n=6 (link:- 2,3,4,5,6 and 1 as frame)

l=0(no slider or rotating pair)

h=0(no higher pair)

Therefore, by Equation of D.O.F by Gruebler, we obtain

D.O.F=3(6-1)-0-0

=3*5

=15

The mobility of linkages shown in fig.1 is\"15\".

2.2) Here, we have a Cam-Follower assembly, this is used for time -chain in various instrument.

From the figure, we can see there are 2 Cams (1&2) pined at respective positions , to produce a line contact along the circumference.( One can see the line contact if viewed from side, along the plane of paper)

Again by Gruebler\'s D.O.F equation,

n= 3 ( 2 Cams and\"1\"frame as the 2 pins are fxed in the same plane )

l=0 (no surface contact,so no lower pair)

h=1( higher/surface pair)

Therefore, by Equation of D.O.F by Gruebler, we obtain

D.O.F=3(3-1)-1

=3*2-1

=5

The mobility of the Cam-follower assembly is \"5\".

2.3) The third figure is a classic example which is a \"Slider-Crank Mechanism\" which is the very basis of every engine ever created (the Conventional engines Ofcourse!!)

From the figure,

n=4 ( crank in this case it is a rotating disc \"2\", the connecting rod i.e link \"3\" , slider \"4\" and the Frame denoted by fixed surface)

l=1 ( the slider with the fixed surface from the surface contact)

h=0 (no higher pairs)

D.O.F= 3(4-1)-2*1

=3*3-2

=7

The slider-crank mechanism has \"7\" degree of freedom.