WOLFRAM

Products
  • Wolfram|One
  • Mathematica
  • Notebook Assistant + LLM Kit
  • Compute Services
  • System Modeler
  • All Products
Consulting & Solutions
  • Wolfram Consulting
  • Industry Solutions
  • Solutions for Education
Learning & Support
  • Wolfram U Courses
  • Wolfram Language Resources
  • Wolfram Community
  • Support FAQs
  • Contact Support
Company
  • About Wolfram
  • Careers
  • Events
  • Educational Programs
  • All Sites and Resources
Wolfram|Alpha
Wolfram Cloud
Your Account
  • Your Account
  • User Portal
Search

Mechanical Systems  / Underconstrained Systems  / Equilibrium Velocity  /
Previous section-----Next section

10.2.2 Finding Equilibrium Velocity

To find the equilibrium velocity of a mechanism, a FreeSystem object is built that contains a new set of equations of motion with one or more constraints removed from the model.

Velocity equilibrium.

The driving constraint is dropped from the slider-crank model to give the model one degree of freedom.

This drops the constraint that controls rotation of the crank.

In[9]:=

This solves the FreeSystem object. Note that the angular velocity of the crank CapitalTheta2d is less than the driven angular velocity of 2 pi.

In[10]:=
Out[10]=

To find the equilibrium velocity at a sequence of positions through a full cycle of the mechanism, the InitialCondition option is used to pass SolveFree a new set of initial conditions at each position where the equilibrium velocity is to be found. Thus, it is not necessary to create a new FreeSystem object for each solution point.

An option for SetFree and SolveFree.

This generates a list of 20 rules to be used as initial conditions for the equilibrium velocity solution.

In[11]:=

This solves the FreeSystem object at each initial condition in postab.

In[13]:=

Here is a plot of the equilibrium velocity of the crank through a full cycle of the mechanism.

In[14]:=

Out[14]=


  • Products
  • Wolfram|One
  • Mathematica
  • Notebook Assistant + LLM Kit
  • Compute Services
  • System Modeler

  • Wolfram|Alpha Notebook Edition
  • Wolfram|Alpha Pro
  • Mobile Apps

  • Wolfram Engine
  • Wolfram Player

  • Volume & Site Licensing
  • Server Deployment Options
  • Consulting
  • Wolfram Consulting
  • Repositories
  • Data Repository
  • Function Repository
  • Community Paclet Repository
  • Neural Net Repository
  • Prompt Repository

  • Wolfram Language Example Repository
  • Notebook Archive
  • Wolfram GitHub
  • Learning
  • Wolfram U
  • Wolfram Language Documentation
  • Webinars & Training
  • Educational Programs

  • Wolfram Language Introduction
  • Fast Introduction for Programmers
  • Fast Introduction for Math Students
  • Books

  • Wolfram Community
  • Wolfram Blog
  • Public Resources
  • Wolfram|Alpha
  • Wolfram Problem Generator
  • Wolfram Challenges

  • Computer-Based Math
  • Computational Thinking
  • Computational Adventures

  • Demonstrations Project
  • Wolfram Data Drop
  • MathWorld
  • Wolfram Science
  • Wolfram Media Publishing
  • Customer Resources
  • Store
  • Product Downloads
  • User Portal
  • Your Account
  • Organization Access

  • Support FAQ
  • Contact Support
  • Company
  • About Wolfram
  • Careers
  • Contact
  • Events
Facebook X Twitch LinkedIn YouTube Wolfram
© 2025 Wolfram | Legal & Privacy Policy |
English
  • en