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TheSchatz Mechanism should move like this

However, with the default solver settings it froze after a few seconds in a planar link configuration. To make it run, I played around with advanced solver settings. Here is one attempt that went nuts:

(More solver settings for strange behavior can be found here:Schatz_Linkage.msim)

Some people might find this amusing. Of course, it is less fun when the initial plan was to spend an hour just for fun with a simple model (an hour is a fair estimate for similar simple looking models in MapleSim). The immediate reaction when seeing such simulation results is to blame the software for being either buggy or incapable. In this case, however, this was not the case, but identifying the root cause was not obvious.

The Schatz mechanism is a so called closed-loop mechanism where the links of the mechanism form a loop (the ground in the model closes the loop). In general, building and modeling mechanisms with loops is less straight forward than thought. Without a-priory knowledge or help (either by documentation or software hints) users can quickly find themselves in a situation of desperate trial and error. What was easy with other models can become a frustrating experience with unsatisfactory outcome. This happened to me on various occasions.   

What makes closed-loop mechanisms more challenging?  After resting for a long time on my virtual pile of unanswered questions, it turned out that the model, on top of being a closed-loop mechanism, is ill-conditioned: The Schatzmechanism is anover-constrained mechanism that is only mobile for certain geometric parameters. MapleSim can simulate such over-constrained mechanisms, but this can be a balancing act for the solver.

Who could have known this? A knowledgeable expert might say that users who do not know what they are doing should not use the software. But how to become aware of over-constrained assemblies when building and running a model in MapleSim does not require to be an expert?  In this case the geometry was taken from a reference that sets the length of the ground link to Ö3. Model build, assembly and simulation instantly worked … but not for an extended time span.

In retrospect, everything is clear. Models that do not assemble do not fit together. Models that freeze in motion “jam numerically”. Linkages and joints of closed-loop mechanisms made of infinite stiff components may not fit together in all geometrical configurations. During runtime, after successful assembly, a stiff model can make a simulation sensitive to numerical errors. This does not mean that the user is dealing with a so-called numerical stiff problem that can be addressed by using stiff solvers. In this case, stiff solvers could not prevent sudden freeze or inversion of movements.

The only remedies that work for infinite stiff and over-constrained mechanisms are the ones that work also in real life. By either introducing mechanical play or elasticity in supports, joints and links, the simulation becomes robust. Numerically, for this case where none of the many advanced solver options made a difference, a simple increase of the relative error in the standard simulation settings worked.  This remedy could be described as introducing morenumerical play. Interestingly in a completely different approach of animating a Schatzmechanism @one man also needed to introduce “deformations” in hissimulation to make it work.

The Schatzmechanism is of little commercial interest and can therefore be shared. Is it a rare case of successful assembly and freeze during runtime or is it more frequent that users run into similar problems? Only MapleSoft can tell, but in the latter case it could make sense that MapleSim supports the user. I see several possibilities for that:

• A more prominent mention in the documentation that kinematic loops require caution could raise awareness.  
• Algorithmically detecting kinematic loops and informing the user that closed loops can be potentially over-constrained in certain geometric configurations.
• (If possible, analyzing the Jacobian in the frozen configuration might give better hints than solver messages during runtime can provide. The attached model gives the hint with MapleSim 2025.1 that the error tolerance might be too tight, but no indication why.)
• Implementing themobility formula, analyzing closed loops and issuing a warning when the mobility M is less than 1 (meaning no degree of freedom)

The latter option sounds appealing. However, the degree of freedom calculated by the mobility formula only provides a necessary but unfortunately not a sufficient condition for mobility.  For example, connecting a prismatic joint coaxially to another increases the mobility by one but does not add to the mobility of a mechanism. This means that an advanced algorithm must take the orientation of joints into account to determine the effective degrees of freedom. On the other hand, the Schatzmechanism and some other mechanisms have a mobility ofM=0 but can be mobile for certain geometries.

Should Maplesoft implement mobility analysis or are CAD tools that offer some sort of mobility analysis more suitable? In my opinion, from a conceptual point of view, it would be beneficial and faster to have this support already in MapleSim before going into details.

Should the user refrain from modeling infinite stiff mechanisms? I do not think so because they are useful in the context of deriving (analytical) forward and inverse kinematics. Furthermore, there are more mechanisms out there that are mathematically, according to the mobility formula, immobile but useful in daily life. Thetelescopic fork is a prominet example.

Final note for math enthusiasts:

The Schatzmechanism (invented by Paul Schatz) is a byproduct of theinversion of a cube. Recalling that the diagonal of the unit cube isÖ3 gives a hint of why the Schatz mechanism becomes mobile for this parameter. Also related to the inversion of a cube is theoloid: a solid with a developable surface that touches with its entire surface a flat surface whenrolling. The oloid and the Schatz mechanism are closely related, which can be appreciated from thisvideo.

Some of the calculations mentioned here can be done in alternative programming languages, such as Python, C, and so on. However, I would like to reproduce exactly these graphs using Maple (without the need for programming commands, such as "if", "while", among others).

In the work I am trying to reproduce, we have "The evaluation of the influence of the inclusion of the broadband behavior of grounding systems in EMT-type programs in the evaluation of transients resulting from direct lightning strikes on transmission lines. The behavior of the grounding frequency is determined using an accurate electromagnetic model and included in the EMTP/ATP by means of an equivalent circuit derived from the Vector Fitting technique. In addition, the impact of the frequency dependence of soil parameters on the lightning performance of transmission lines is addressed." This may seem somewhat disconnected from reality for many, since it is a problem involving electrical engineering optimization.

Could someone help me reproduce these calculations? I have made little significant progress.

If you want to access the reference accounts, I'll send you the PDF

schroeder2017 [link to copyrighted material replaced by moderator]

This post summarizes links for those who have not studied numerical integration methods from scratch and are interested in simulation settings in MapleSim (like me).

The MapleSim help pagessimulation settings andadvanced simulation settings give first guidance for the trained user but do not provide explanations or links for the terms used in the description of the settings (as for example: stiffness, constraint stabilization, constraint projection, events and event iteration,...).

It can easily be overlooked that Maple help pages provide further information for most of the terms. Under the assumption that MapleSim uses the same terminology as Maple, I recommend to first have a look at Maple help topics before consulting the web or other resources. Since searching and retrieving can be time consuming, I made a list of helpful links.

There are still someopen points. I would be happy for more links and help in filling these gaps.

How Maple simulates

?MapleSimUserGuide,Chapter04:
section4.1 How MapleSim Simulates a Model

?tasks,generatingCode

Solvers

An overview of solvers:?dsolve,numeric

Differential Algebraic Equation introduction:?MaplePortal,DAE

Overview of numeric differential-algebraic equation solvers (index reduction, constraint drift, projection):
 ?examples/numeric_DAE and?dsolve,numeric,DAE_extension

Stiffness and stiff solvers

Stiffness and stiff IVPs:?dsolve,Stiffness

Events

?dsolve,numeric,Events

Time events andstate events

Event handling:

?MapleSimUserGuide,Chapter04:
section4.1 How MapleSim Simulates a Model

Event iteration:

?MapleSimUserGuide,Chapter05:
section5.5 Selecting the Code Generation Options

Iteration, hysteresis, Intermediate steps:?tasks,generatingCode

Hysteresis:

Hysteresis in value or also in time?

Do variable solvers adapt the value of event hysteresis during runtime?

Baumgarte constraint stabilization, unconstrained dynamics, constrained dynamics

?MapleSim,Multibody,Dynamic_Exports
(in combination with?MapleSim,Multibody,Kinematic_Exports)

?examples/numeric_DAE

?tasks,generatingCode

?MapleSimUserGuide,Chapter05:
section5.5 Selecting the Code Generation Options

Error control

             ?dsolve,numeric,Error_Control

              Absolute error:?dsolve,numeric,IVP

              Relative error: (relative to what?)

Index1 error control and Index1 Tollerance: see solvers

Scaling

scalemethod(this does not seem to exist inMaple)

Examples (Multibody)

Events

                            Catapult
                            (from MapleSim>Help>Examples>Physical Domains>Multibody)
                            contact events

                         Catapult_-_Events.msim

                            Throwing a ball
                            (from MapleSim>Help>Examples>Physical Domains>Multibody)

                            conditional events (with boolean logic)

                          Throwing_a_Ball_-_Events.msim

             Solvers

              Conservation of energy of a pendulum depends on solvers.
                           Euler increases energy, implict Euler dissipates energy.

            Pendulum_for_solver_comparision.msim

Constraint dirft/projection

              2-d rigid slider crank

               (from MapleSim>Help>Examples>Physical Domains>Multibody)

              projection off leads to assembly desintegration after 2000 s simulation

            2D_Rigid_Slider_Crank_-_constraint_projection.msim

                         A stiff solver improves constraint drift, but only delays desintegration

                         Baumgarte constraint stabilization prevents simulation error but shows dislocated rigid body frames

ac-dc-dc1.msim

When i click off the "Plot events", the figure of Probe2 is pretty different comparing with "Plot events" is turned on. Here is my assumption: the simulation duration is 500 seconds and the plot points are 2000. Considering the frequency of sine current is 40HZ, many points cannot be ploted in the figure. So it is not a big deal for curve like Probe1 and Probe5 because  they tend to be a constant and Probe2 just reflect the tendency.

I try to design a half rectifier circuit in MapleSim, but the simulation is so slow and the console output says "Warning: many small integration steps are being taken at a very small proportion of integration range at t=2.9653230e-006, absolute/relative tolerance may be too tight for problem, or problem may require a stiff solver". So how should i improve the circuit to make the simulation faster?

By the way, i don't want to change the basic design of the circuit, so the circuit should consist of both diode and op amp. I know the diode only circuit can achieve the same goal.

half_rectifier.msim

I am wondering if there are examples of agent-based models in economics domain that have been implemented in Maple.

Any infomration/source is more than welcome!

Thanks in advance

Hi

I am trying to construct a controler for a UR5e robot, I have a simulation of the robot in maplesim and have started to look for a way to use multibody analysis to provide me with the Jacobian. However it only provieds the constraint Jacobian and as I have no position constraints on the robot, it returns nothing.

I then came across 

Link: https://www.youtube.com/watch?v=d3xJge_09E0&t=374s

However it is old and does not exactly say how to do it.

So I thought I should ask this wonderful comunity if they have an recomended way to construct the Jacobian from a maplesimmodel? I am still a beginner at maplesim and maple so any help is appreciated.

With thanks for helping me

Eric Ragnarsson

In the present work we are going to demonstrate the importance of the study of vector analysis, with modeling and simulation criteria, using the MapleSim scientific software from MapleSoft. Nowadays, the majority of higher education centers direct their teaching of vector analysis in an abstract way and there are few or no teachers who carry out applications using modeling and simulation. (In spanish)

IPN_CICATA_2020.pdf

Expo_MapleSim_CICATA.zip

Dear Community,

I have a simulation in MapleSim, and I have a probe in the system, for which measured data are also available. How can I load these measured data into MapleSim and compare them to the calculated results (probe data) visually? (Preferably in the "Analysis Window: Simulation Results" which pops up by pressing F6)

Tx for the kind help in advance,

best regards,

Andras

Application of MapleSim in Science and Engineering: a simulationbased approach

In this research work I show the methods of embedded components together with modeling and simulation carried out with Maple and MapleSim for the main areas of science and engineering (mathematics, physics, civil, mechanical etc); These two latest scientific softwares belonging to the company Maplesoft. Designed to be generated and used by teachers of education, as well as by university teachers and engineers; the results are highly optimal since the times saved in calculations are invested in analyzes and interpretations; among other benefits; in this way we can use our applications in the cloud since web technology supports Maple code with procedural and component syntax.

FAST_UNT_2020.pdf

kinematics_curvilinear_updated_2020.mw

Lenin AC

Ambassador of Maple

Here we simulate the motion of a container with a flat bottom that can slide on a horizontal surface subject to dry friction (Coulomb friction).  Installed inside the container is an ordinary mass/spring/damper system where the mass slides horizontally.  We impart an initial velocity to the container.  That sets the mass into motion which then affects the container's motion.  Under certain conditions the container will undergo a stick-slip motion which is evident in the simulation.

This simulation very roughly approximates the motion of a partially filled bucket of water that slides on the floor when kicked.  The idea arose in a discussoin with Carl Love and mmcdara:
https://www.mapleprimes.com/posts/211677-Mass-Spring-Conveyor-Belt-And-Dry-Friction

In the animation below, the container is shown in dark color when it slides against the floor, and light color when it sticks.

Worksheet: slosh.mw

Application developed using Maple and MapleSim. You can observe the vector analysis using Maple and the simulation using MapleSim. Also included a video of the result. It is a simple structure. A pole fastened by two cables and a force applied to the top. The results are to calculate tensions one and two. Consider the mass of each rope. In spanish.

POSTE_PARADO.zip

Lenin Araujo Castillo

Ambassador of Maple

Analysis in Dynamics of Structures with Maplesim for Engineering
Here is the power of Maplesim in modeling and simulation. With Maplesim you can model structures at rest and dynamics. Considering real patterns of our world for better optimization.Project developed for students of Civil Engineering, Architecture, Mechatronics and all those professional careers related to structures.

CIMAC_UNALM_2019.pdf

Lenin Araujo Castillo

Ambassador of Maple

The simple approach from Peter (creating a custom modelica component) is to getting started by running a simple simulation where x_dot(t) = - a*x,  where the normal form is x(t) = x^-a for logarithmic type decay.

plot of x(t) should be a decay curve.  

Maple Code

A:-LinkModel = fine, connects

***********

Simcode

Model Main;

Imports

end Main;

Consider a wave y=f(x,t) with amplitude modulation such that it becomes

 y_new=(1+A)*f(x,t), where A=A(t) is a small perturbation.

How can I do the simulation to test the robustness of the system to see if the wave is stable / unstable under perturbation? As the time t goes to infinity, I want to see if the original wave is distorted or not under either random or prescribed perturbation.

P.S. For example,  f(x,t) = (sech(0.5*x-0.1*t))^2.

Thank you for your help.