Transfer functions are normally not used with units. Involving units when deriving transfer functions can help identify unit inconsistencies and reduce the likelihood of unit conversion errors.

Maple is already a great help in not having to do this manually. However, the final step of simplification still requires manual intervention, as shown in this example.

Download Collecting_and_expanding_units.mw

A failing slinky is another intriguing physics phenome that can be easily reproduced with MapleSim.

The bottom of a vertically suspended slinky does not move when the top is released until the slinky is fully collapsed.

To model this realistically in MapleSim, it is necessary to

• Establish a stretched equilibrium state at the start of the fall
• Avoid penetration of windings when windings collapse (i.e. get into contact)

The equilibrium state is achieved with the snapshot option. Penetration is avoided with the Elasto Gap component. Details can be found in the attached model.

A good overview of “Slinky research” is given here. The paper provides a continuous description of the collapse process (using an inhomogenous wave equation combined with contact modeling!!!) and introduces a finite time for the collapse of all windings. Results for a slinky are presented that collapses after 0.27s. The attached model has sufficient fidelity to collapse at the same time.

Real Slinkies also feature a torsional wave that precedes the compression wave and disturbs an ideal collapse. This can be seen on slowmo footage and advanced computer models. With a torsion spring constant at hand (are there formulas for coil springs?), it could also be modeled with MapleSim.

Falling_slinky.msim

Maple allows to extract, manipulate, and optimize equations from a MapleSim model. Code can be generated from the equations in various programming languages. To verify the code, C code can be imported back into the original MapleSim model and compared to the model.

This verification step is not an everyday task, but it is advisable before the code is used elsewhere (e.g., in a controller). This post summarizes helpfull links and provides an additional example with equations that are too large to be efficiently verified by code review.

Comparison to a physical model is demonstrated here on an older version of MapleSim (~2015). In newer versions the import has changed (basics are described in Tutorial 6.6: Using the External C Code/DLL Custom Component App). An external C compiler must be set-up to make the import work.

The attached MapleSim model verifies against an optimized custom component. Instead of manually entering and modifying the code as described in the Tutorial 6.6, the model uses a Maple worksheet that programmatically generates C code from Maple equations and modifies the C code (sets C definitions and parameters) to be usable for MapleSim’s External C/Library Block App.

The Maple worksheet to generate and modify C code has been improved in many details with support from MaplePrime users for which I would like to express my thanks.

C_code_generation_of_optimised_code_for_MapleSim.mw

C_code_generation_of_optimised_code.msim

I have polished up findings with custom components to share it here:

Optimized code generated with Maple’s codegen package cannot be used in the same way as it was possible with older versions of MapleSim’s Custom Component Template.

Intermediate variables `tx` (where x is an integer) of the optimized code are interpreted as physical parameters in the current template version and not as variables. This makes sense and is more consistent with MapleSim’s definition of variables and parameters, but leads to errors in MapleSim.

The attached model shows how optimized code can be generated for the current template and compares an older, still working (!) template with the new one.

The attached worksheet contains commands to programmatically generate optimized code for the current Custom Component Template.

CustomComponentTemplates_comparision.msim

Optimized_code_for_custom_component_template.mw

Combing a Prismatic Joint component with an Elasto Gap component does not always provide correct results. Incorrectly combined (red mass below), a force is generated although the distance between the flanges is greater than the relaxed spring length. A force is exerted (instead of no force is exerted as stated here) on the mass which leads to a smaler deflection (expected are 9.81 m).

This happened to me although I connected flange_a to flange_a and flange_b to flange_b in configruation A bellow. Configuration B works with inverted flanges and configuration C works with inverted unit vector of the prismatic joint. By reversing the direction of gravity, configuration A becomes a valid configuration and configurations B and C become invalid configurations.

It seems that in invalid configruations the value of the  flange distance s_rel can have a large magnitude but is negative in sign which generates significant forces although there is no contact of flanges.

So far for the observations.

Would a change of the contact condition

prevent invalid configurations or do we have to live with it for principal reasons that I am over looking?

If so, I don't see a foolproof method to avoid invalid configurations. Instead, I can only suggest measuring the flange distance of the Elasto Gap component as in the attached. If negative values of large amplitude occur, the configuration is invalid.

Assuming that a beginner would connect intuetively flange_a to flange_a and flange_b to flange_b, there is a chance of 50% that the configuration is invalid (A instead of C). This is too much to be acceptable, especially since verifying results in complex assemblies is often not possible.

It is worth noting that the contact condition comes from the underlying Modelica component and not from MapleSoft.

Prismatic_Joint_with_Elasto_Gap.msim