# Degree of freedom of a mechanism

A mechanism popped up in my mind when I was studying kinematics, see picture below $$J1,\ J2,\ J3$$ are rotational joints and there are two translational joints $$J4$$ and $$J5$$ between two sliders and the cross hatched rail. Sliders are free to move horizontally towards or away from one another. Now when I imagine a motion in which a force is applied vertically at $$J1$$, pushing or pulling on the said joint, thus sliders move away or come closer, I think it is a one degree of freedom mechanism. However the famous formula $$3n-2j-3$$ where $$n$$ is the number of links and $$j$$ is the number of lower pair joints, gives two degrees of freedom. Considering the rail as a ground link, with two sliders and two arms ($$J1J2$$ and $$J1J3$$) we have $$n=5$$ and we have $$j=5$$

$$3*5-2*5-3=2$$

So, what is with that?

• I imagine a motion in which a force is applied vertically at J1, - and what happens when you apply force at J1 horizontally? How does sliders move then? – elementiro May 18 at 23:05
• @elementiro They would move in the direction of that horizontal force, but their motion will still be dependent. Am I wrong? – Ali Kıral May 18 at 23:39
• If you can't represent that movement as the sum of multiplies of movements in already established degrees of freedom then it isn't dependent. For the first DOF you've denoted displacement of J4 is opposite to displacement of J5 but equal in absolute value. Does it stay the same when the sliders move in direction of the force? – elementiro May 19 at 9:18
• @elementiro I was missing the horizontal motion of J1 all along, I understand now – Ali Kıral May 19 at 21:51