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Equations for two stage scissor jack

Equations for two stage scissor jack

(OP)
Hello, I have a two stage scissor jack likes the one shown in the photo but with the addition that a DC motor is connected to the knob. Could anybody please show me how to obtain the dynamics equations for this system? Thank you

https://en.wikipedia.org/wiki/Laboratory_scissor_j...

RE: Equations for two stage scissor jack

Use the first and second derivatives of the equations of motion to get the kinematics, then multiply by the masses and the polar moments of inertia to determine the forces.

RE: Equations for two stage scissor jack

Kinematics is the hard way. There is only one motion input and one motion output. You can do this with a power balance.

Power required to lift is weight times speed (yes you need to know how fast). This tells you the ideal (frictionless) motor power required. FYI power is torque * rotation speed.

Determining friction... that's something you need to measure, most likely. If you can't do that then start with double your ideal power requirement for the motor.

RE: Equations for two stage scissor jack

there have been lots of threads on scissor jack loads, maybe search for them ?

As posted above, the equations should be easy to derive ... single input (turning the knob), single output (raising the platform). I'd start with a small rotation of the knob produces what changes to the scissor jack ? Then you can determine the work done by that small rotation and so the work required to turn the knob.

another day in paradise, or is paradise one day closer ?

RE: Equations for two stage scissor jack

(OP)
I searched many books and websites but there is no example on such system. How come?

RE: Equations for two stage scissor jack

it may be that most scissor jacks are more "industrial" in size, maybe operated by hydraulics, but the principles are the same.

I'd've thought your configuration (with a screw drive through the scissor joints) is easier to analyze ...
turn the knob, change the distance between the two fittings mounted to the thread, change the height of the platform (and also change the height of the CG of the scissors).

I think you've got two things to worry about with your motor ... the work required of it (ie the torque) and the rate of work (ie Power).

another day in paradise, or is paradise one day closer ?

RE: Equations for two stage scissor jack

Kinematics is the first step to analyze the entire mechanism. Even the virtual work method still requires developing an equation that relates the input to the output, which is a non-linear one for scissors jacks.

RE: Equations for two stage scissor jack

Yes and no. You would be surprised at how little kinematics matter in arriving at a solution. I've done it, but there are more effective ways.

With systems like these, I usually looked the system in a best and worst positions, and determined mechanical advantage from small movements (e.g. 1/4 turn of shaft or 1mm vertical movement). Simple enough to get this from a 2D CAD sketch. Comparing resulting torque or force to performance curve of an actuator or motor provides results that are as dependable as the said performance curves (here's where you find out how honest your motor manufacturer was).

RE: Equations for two stage scissor jack

Tick - so you are using a graphical kinematic analysis tool?

RE: Equations for two stage scissor jack

Until OP defines what he means by dynamics equations then we are possibly talking at cross purposes.

I have no issue with using virtual work to figure out Fout vs Tin for a given geometry, or platform speed vs rpm, but that ain't dynamics.

Cheers

Greg Locock


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RE: Equations for two stage scissor jack

@3DDave

Done it all: kinematics, simulation, test fixture, product, etc. Had a job where I had to figure this stuff out for linear actuators on hospital beds. Classic kinematic stuff.

Nothing wrong with doing the kinematics. I can do it. It's just that it's usually the long way, and prone to errors and doubt. For a case like this I would do one of two things:
  • Measure the input/output actions on a specimen
  • Get mechanical advantage from a 2D sketch (e.g. in SolidWorks)

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