Purple links 3legs 10cm Yellow links 2 1438cm Red link verti

Solution

(2) Degree of Freedom (F) = 3 (n-1) - 2j1 - j2

where n = number of links with frame. = 8

j1 = Joints with single (one) degree of freedom. = 1

j2 = Joints with two degrees of freedom.= 0

Thus F = 3 (8 - 1) - 2(1) - 0

= 21 - 2

F = 19

(3)  Grashoff\'s law:

Grashoff 4-bar linkage: A linkage that contains one or more links capable of undergoing a full rotation. A linkage is Grashoff if: S + L < P + Q (where: S = shortest link length, L = longest, P, Q = intermediate length links). Both joints of the shortest link are capable of 360 degrees of rotation in a Grashoff linkages. This gives us 4 possible linkages: crank-rocker (input rotates 360), rocker-crank-rocker (coupler rotates 360), rocker-crank (follower); double crank (all links rotate 360). Note that these mechanisms are simply the possible inversions of a Grashoff mechanism.

Non Grashoff 4 bar: No link can rotate 360 if: S + L > P + Q

Grashoff condition

Consider a linkage with the shortest and longest sides joined together. Examine the linkage when the shortest side is parallel to the longest side (2 positions possible, folded over on the long side and extended away from the long side). How long do 1 and 2 have to be to allow the linkage to achieve these positions?

Consider a linkage where the long and short sides are not joined. Can you figure out the required lengths for 1 and 2 in this type of mechanism.