Mechanics, degree of freedom question

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SUMMARY

The discussion focuses on calculating the Degrees of Freedom (DoF) for a mechanical system using the formula M = 3(L-1) - 2J1 - J2. The user identifies 9 links and 1 half-joint, but is uncertain about the number of full binary joints, particularly concerning the slider mechanism. The conclusion drawn is that there is likely only 1 DoF, attributed to the rotational movement of a circle at the top of the system. Clarifications are sought regarding the nature of the connections between strings and their implications on mobility.

PREREQUISITES
  • Understanding of Degrees of Freedom (DoF) in mechanical systems
  • Familiarity with joint types: full binary joints and half joints
  • Knowledge of mechanical linkages and their configurations
  • Basic principles of kinematics in mechanical engineering
NEXT STEPS
  • Study the application of the formula M = 3(L-1) - 2J1 - J2 in various mechanical systems
  • Explore the characteristics and calculations of full binary joints and half joints
  • Research the mechanics of slider-crank mechanisms and their Degrees of Freedom
  • Investigate the implications of string and pulley systems in mechanical design
USEFUL FOR

Mechanical engineers, robotics students, and anyone involved in the design and analysis of mechanical systems and linkages.

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Homework Statement



Calculate the DoF (mobility) of the following system:

3026041de8b9529d84160ec6964b3ec4.png


Homework Equations


[/B]
M = 3(L-1) - 2J1 - J2

(where L = number of links, J1 is the number of full binary joints and J2 is the number of half joints.

The Attempt at a Solution



I am very confident about there being 9 links, and 1 half-joint (the pin in the slot above the L link) but I am unsure about the number of full joints which I numbered here.

2b60e7e0a8424c6c6a8b32d4ec9c2d8a.png


I know from 1-7 should be correct, but I don't know about the joints on the slider. Should there only be two binary joints for each like I put there? Which is basically one ternary joint... 2 on the rigid link 'L' and on the link to which the slider is attached.

And if I am correct I take it there is only 1 DoF then, which is the rotational of the circle attached to the top?

Help would be appreciated here.
 
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I presume the straight lines are strings. What happens when two straight lines meet at a little circle? Is it a pulley? Is it a post to which they are knotted? What about when three strings meet at a little circle? Can the little circles move?
 

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