In the last post about the crane, “Using CAD in initial design – More work on the Popsicle Crane“, we determined all of the angles necessary to calculate the forces on all the beams and cables. In this post I will calculate all those forces based upon that initial design. Things will change… they always do. If one were to plot the design completion on a graph, the plot would look very similar to exponential curves we have been using to show voltage across a capacitor. The work goes fast at the start and then slows down in the detailed design.
To do the calculations, free-body diagrams were created for points at the end of the main boom and the point at the top of the “hinge boom”. (Refer to Episode 25 – Introduction to Statics and Forces on a Beam for more information about free-body diagrams.) Starting from the load, the weight hanging at the end of the hook, I then divided the forces into two components. A component running down the beam, and a component making the beam want to turn around the hinge pin at then base end of each beam. The goal was to work backwards and determine the forces on each cable.
I created a spread sheet, crane_ang.xls available for download, to calculate the forces required on each of these elements at boom angles. A shortened version is shown to the left. Above the yellow line, I show the data obtained from the CAD drawings. The first column of the spread sheet describes the angle. The second column is the name I assigned to a variable to permit me to use it in future descriptions of the calculations. The numbers in columns C to E of this shortened version are the angle values inputted from the CAD drawings.
Below the yellow line in the first picture is the free-body calculations for the end of the main boom. The top half is the set describing the rotation of the boom around the hinge and the second half is the compression on the boom. The text in each of these describes the calculations used. I recommend that you sketch these diagrams and attempt to follow the calculations to truly understand what I was doing.
Once the force was calculated on the main “guy wires” holding the boom. I then moved on to the “hinge boom”, the new structure to be built behind the main main boom. As expected, the forces become much much higher as the main boom is lowered.
To build this 2nd boom I will probably move away from popsicle sticks and build it out of some sort of wooden structure and possibly with steel rods to serve as the pulley axles. The force for the “pull down cable” on the hinge boom is very very high. I will probably use a series of pulleys there to gain a 10:1 mechanical advantage. This seems to be very similar to what is done on all the real cranes I have looked at that still use cables in this area. (Many use hydraulic cylinders here.)
Because I am feeling confident the crane can handle it, the present goal is to be able to handle 10 lbs on the hook at all boom angles greater than 5 degrees. The weight can be increased at higher angles.
As a final note, I have found some wire rope that is both flexible enough and strong enough to become the main guy wires supporting the main boom. Attaching these to the hinge boom is one of the things I am currently thinking about. Ideally, I want to use a pulley like I did in the test to make sure the two cables share the load. One of the major problems of implementation will be to make sure the hinge of the this new boom, the hinge boom, is exactly aligned with the main boom hinge. If it is not then as the two booms swing the length of the two cables running from one boom to the other may change in relationship to each other causing one cable to take excess load. If I am able to put in pulley in the system these two will share the load and the main boom will not have a bending stress on it…… More details…. It is all about details!
I will not post anymore about the crane until I get significantly more work completed.
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