Discovering the Mobility of the Pictured Mechanism: Analysis and Insights

[nakos922]

I need to find the mobility of the pictured system
I have labeled the 5 links with black numbers and the 6 joints with red letters for convenienceAttempt at a solution: I know the mobility equation is M = 3(N-1) – 2(J1) – J2 + R, where N = number of links, J1 is the number of 1 DoF Joints, J2 is the number of 2 DoF joints and R is the number of redundancies.

So far, I have 5 links (where 1 is the ground and 4 is the entire disk), 5 1 DoF joints (A, C, D rolling without slipping, E & F), and one 2 DoF joints (B, a 2 DoF slider).

Plugging that into the mobility equation yields 3(5-1) – 2(5) – 1 = 12 – 10 – 1 = 1

However, upon inspection, the system has 2 degrees of freedom and not 1 as the mobility equation suggests. I have been trying to reason through where I may have went wrong, or if there are any redundancies in the system to no avail. Any help would be appreciated.

 

[Tom.G]

Does it help if you visualize the disk mobility if link 3 does not exist?

 

[nakos922]

Would link 3 be redundant since the position/rotation of the disk already has only 1 DoF due link 5 and the ground (link 1/joint D)? Then you have 1 DoF due to link 2 which wouldn't be connected to anything else, so a total of 2 DoF for the mechanism with one redundancy.

Am I on the right track with that logic?

 

[Tom.G]

Unfortunately I have no idea!
I found the problem 'interesting' and studied the drawing for a while. I realized that joints A, B, C were free to rotate and link 2 could have any arbitrary length. That implied they did not constrain the location of joint C.

Hopefully someone else on the site can evaluate your formal evaluation. Im' an electronics guy and most of my mechanics is what I've picked up along the way.

 

[Kajan thana]

I am getting the mobility to be 1 where the n = 6 j= 7 and high pair = 0

 

[Tom.G]

Let's see if we can get an expert in on this.
Paging @jrmichler

 

[jrmichler]

Five year old thread!

However, upon inspection,

The OP's calculation appears to be correct. The OP's problem is understanding why that is the case. Here's how I look at it:

1) The disk 4 is triangular link DCE because there is no slipping at D.
2) The link 5 locks link DCE in position, therefore link 3 pivots around fixed point C.
3) If link 3 has a pivot at slider B, and link 2 has a slider connection at B, then slider B has one DOF.

Side note: I last saw this calculation as an undergrad in the 1970's. But understanding the concept of number of constraints and resulting degrees of freedom has been very important since then.