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Welcome
What's New
View new features for MotionSolve 2024.
Overview
MotionSolve^® is an integrated solution to analyze, evaluate, and optimize the performance of multibody systems.
Tutorials
Discover MotionSolve functionality with interactive tutorials.
MotionSolve User Guide
MotionSolve is a system level, multibody solver that is based on the principles of mechanics.
- Introduction to MotionSolve
- Platform Support, Recommended Hardware, and Licensing
- Run MotionSolve
- Model Systems
- Model Simulations
- Visualize Results - Animation and Request Plots
- Couple MotionSolve with Other Software
- Customization Capabilities
- Analysis Tips
- NLFE Bodies Introduction
- User Subroutines in MotionSolve
- msolve API
- MotionSolve Verification Manual
- MotionSolve Optimization Guide
  - Introduction
    The MotionSolve Optimization Guide explains the design sensitivity and optimization capabilities in MotionSolve.
  - Optimization Capabilities in MotionSolve
    Optimization capabilities in MotionSolve include equations of motion for a multibody system, design variables and limits, and analysis support.
    - Equations of Motion for a Multibody System
      This section describes equations of motion.
    - The Optimization Problem Formulation
      Optimization algorithms work to minimize (or maximize) an objective function subject to constraints on design variables and responses.
    - Design Variables and Limits
      Design variables are used to define parametric models.
    - Response Variables
      Model behavior is captured in terms of Response Variables.
      - DeviationSquared
        Computes the square of the difference between a function’s value at a certain time and a desired value.
      - GenericResponse
        Defines a generic response. This is the same as the MSOLVE API Rv element.
      - ResponseExpression
        Computes the value of a user specified function.
      - MaxVal
        Computes the maximum value of a user specified function, which could be a MotionSolve expression or a user subroutine.
      - MinVal
        Computes the minimum value of a user specified function, which could be a MotionSolve expression or a user subroutine.
      - RMS2
        Computes the root mean square area difference between a measured signal and a target curve.
      - Slope2
        Computes the slope of a measured signal at a point of interest x*.
      - Slope2Deviation
        Computes the square of the deviation of the slope of a curve at a certain point in time from a target value. A finite differencing scheme is used to compute the slope.
      - ValueAtG
        Computes the value of a signal f (t) when second signal, g (t), achieves a certain value.
      - ValueAtTime
        Computes the value of a signal at a particular time, T=t*.
      - maxVal
        Computes the maximum value of a signal during a simulation.
      - minVal
        Computes the minimum value of a signal during a simulation.
    - Sensitivity Calculation
      The sensitivity of an output y (u) to an input u is defined as the change in y due to a unit change in u.
    - Scaling Mechanism
      Both Dv and Response can be scaled in msolve.
    - Analysis Support
      MotionSolve supports DSA only for Kinematic, Static, and Quasi-static analyses
    - License Usage for Optimization Jobs in MotionSolve
      The optimization capability in MotionSolve typically involves several solver simulations - one to determine sensitivities for the initial design and several consequent design simulations to determine and adjust design variables based on responses to satisfy the overall optimization criteria.
    - Optimization Problem Formulation and Solution
      Topics in this section include optimization problem types and optimization search goal and methods.
  - Application Areas
    Optimization is a vast area that has a many applications in diverse areas such as engineering, economics, business and medicine.
  - Optimization Input Data
    The input data for an optimization is organized in a python parametric model class with methods that operate on the class.
  - Optimization Output Data
    Every optimization run generates a variety of files.
  - Advanced Topics
    Advanced topics include a scaling optimization problem and tips on how to debug optimization runs.
  - SLA Suspension Example
    This example, referred to as MV3010 in this section, describes the optimization of an SLA suspension and is also available in MotionSolve tutorial topics/solvers/ms/optimization_using_mv_hs_intro_r.html.
  - PID Controller Example
    In this example, we are designing a PID controller whose job is to minimize the effects of a disturbance force on the position, velocity, and acceleration of a block.
  - Glossary
- MotionSolve Environment Variables
- References
MotionSolve Reference Guide
This manual provides a detailed list and usage information regarding command statements, model statements, functions and the Subroutine Interface available in MotionSolve.

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MaxVal

Computes the maximum value of a user specified function, which could be a MotionSolve expression or a user subroutine.

The maximum value of a signal $f (q (t))$ satisfies the following condition: If T* is the point in time when is $f (q (t))$ maximum, then $f (q (T *)) \leq f (q (t))$ when t ≠T*. If the expression has no maximum value, the initial value will be returned as the maximum value.

A smooth approximation to the MAX function is implemented in MotionSolve, so that its sensitivities are analytically computed. The smooth approximation, known as the alpha soft approximation, is:

$M a x v a l (x) = \frac{\int_{0}^{T} x (t) e^{a x (t)} d t}{\int_{0}^{T} e^{a x (t)} d t}$

The parameter

$a > 0$ is used to control the accuracy of the calculations.

Note:

$M a x (x) = \lim_{⍺ \to \infty} M a x v a l (x)$ .

The default value of $a$ is +10 and it should work for most of use cases.

Example

Assume that you are designing a suspension system and there is an upper limit on the maximum acceleration of the chassis.

Here is a code snippet that shows how the response should be defined with MaxVal:

>>> # Define the maximum of acceleration
>>> maxAcc = MaxVal(function = "ACCZ({})".format(p.cm.id))