Machine Dynamics, Solved Problems, Linkages, Mobility of a mechanism, Problem 6
12#Theory_of_Machines #Mechanical_Engineering #Kinematics
This video is part of a series of videos presenting solutions of problems related to the machine dynamics topic.
In this video, we will calculate mobility of a mechanism involving an important number of links.
And also involving rotating joints of second order.
In this problem we are asked to determine the mobility of the mechanism shown here.
First, we need to determine, L, the number of links or the number of mechanical parts, in the mechanism,
Second, we need to determine, j 1, the number of lower pairs, or the number of joints allowing each, one degree of freedom,
Third, we need to determine, j 2, the number of higher pairs, or the number of joints allowing each, two degrees of freedom,
Finally, we will calculate mobility M, as 3 times L minus 1, minus 2 j 1, minus j 2.
This mechanism is built from,
The ground or the frame.
A quaternary link.
Four sliders.
And 12 bars,
Thus, L is equal to 18
In this mechanism there are four translating or prismatic kinematic pairs.
One pair between each slider and the ground.
We will have also 12 rotating or pin kinematic pairs.
However, some are simple connecting two links each,
And some are o second order connecting 3 links each and thus they should be counted twice each.
Here the rotating joints connecting the quaternary link to the bars 7, 10, 13 and 16 are simple.
Each should be counted once.
All the remaining 8 rotating kinematic pairs are of second order.
Thus each one should be counted twice.
In all we have four translating joints, four simple rotating joints, and 8 rotating joints of second order.
Thus, j 1 is equal to 24.
The mechanism does not involve any higher kinematic pair, hence, j 2 is equal to 0
Substituting the value of L, j 1 and j 2 in the equation of mobility gives M is equal to 3.
Here, three degrees of freedom can be controlled independently.
For example, it is possible to control independently three sliders out of the four.
The mechanism should receive three inputs.