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  • Need help optimising and solving loading in a pinned 3 strutted linkage

    Discussion in 'Calculations' started by ThomasG, Nov 15, 2012.

    1. ThomasG

      ThomasG New Member

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      Hi all,
      I have quite a specific problem and I was hoping to get some help. Or maybe just some pointers regarding how to progress with this design challenge. Unfortunately it’s been a couple years since I last did and static loading and I don’t know how to get to a solution. This is a very small system with applications in the medical industry.

      So here’s the problem:
      There is a single beam with 3 struts attached to it (pin joints). These 3 struts are in turn attached to 2 sliding shafts (pin joints) so that by moving one of the shafts axially you will force the beam to extend away from the cylinders or contract towards the cylinders. Figures explaining the set-up are attached.

      The idea here is that an axial force applied to the green cylinder will cause the beam to extend or contract parallel to the cylinder. The beam will be under a constant uniformly distributed load (may be generated by a pressure). I would like to solve the problem for the entire range of strut angles using an excel spreadsheet.
      So my question is threefold:
      a) What is the optimum configuration for these struts? Two at -45° and one at +45°; all at the same angle, etc.)
      b) What is the optimum spacing for these struts considering the total length of the beam is 40mm? (The cylinders can be shorter/longer than the beam)
      c) What is the maximum force that the struts will see with a uniformly distributed load of 0.3 bar acting downwards along the length of the beam?

      Specific considerations and assumptions:
      1. System must expand and collapse in parallel i.e. the beam must be parallel to cylinders.
      2. Friction can be assumed negligible.
      3. All joints are pin joints with a diameter of 0.7mm.
      4. Ignore component interferences
       
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    3. Erich

      Erich Well-Known Member

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      Attachments did not come through.

      I cannot visualize the configuration of your elements.

      The general approach to the problem is to isolate each piece of the mechanism and draw a Free body diagram with all the forces acting on each body.
      Sum the forces in X and Y and set equal to zero.

      If your mechanism is statically determinate, you will end up with a system of N equations and N unknowns.

      A lot of algebra later you can solve for your forces.

      Be careful about assumption 2. At low angles between your power cylinder and the linkages, the pin friction can make the mechanism lock up.
      Been there, done that, got to do it again. (Properly)
       
    4. ThomasG

      ThomasG New Member

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      Hi Erich - thanks for the quick reply!! I have uploaded the pictures and anther description of the problem to the instructables website as I couldn't figure out how to do it here! Heres the link:

      http://www.instructables.com/id/Strutted-Linkage-Problem/

      You also seem to have experience with this kind of design (i am very green!). If you have suggestions for gaining mechanical advantage at small linkage angles that would be great!


      From instructables blog..
      One final question that I am struggling with but any help would be appreciated. At very small angles (between the power cylinder and the linkages) the force needed is very large. I am exploring using a secondary device or additional construction to provide mechanical advantage to reduce the force needed. Any suggestions will be welcomed!!!


      Thanks!!!
       
    5. Erich

      Erich Well-Known Member

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      I don't think that assembly of linkages is going to work very well.

      cylinders, air or hydraulic are NOT designed to tolerate side loads on the shaft. The angled linkage that connects the cylinder shaft to the platform will put considerable side load on the cylinder. A sure recipe for binding, leaks and short life of the cylinder.

      I would attach the end of the cylinder shaft to the platform with a pin joint. The other end of the cylinder attaches to a base plate with pin joint as well. The two parallel links that control the motion of the platform now need to attach to the same base plate the cylinder attaches to.
       
    6. joansans

      joansans New Member

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      ThomasG,

      I think that Erich is ok with their observations, but you can modify your design and add something to absorb the radial forces that will act on the cilinder. In standard cylinders, some manufacturers put two bars in paralel with the rod. This is an example.

      You can find, rougly, the relation between input and output forces, apliying virtual power method. You will found the maximum value by solving the kinematics of the linkage and doing In_velociy*In_force+out_velocity*out_force=0. You must take into acount the sign of the vectors you are using. You can apply this method taking into account inertias and you will find motion equation to solve completelly the problem. I hope I help you!
       

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