Four Bar Linkage Solution Fail: Freudenstein

Questions
, ,
1

First, go easy as I’m a new Mathematica user and clearly on the steep part of the learning curve. :slight_smile:

I am trying to solve an equation that relates to a four bar linkage commonly used in mechanical engineering. It is governed by the Freudenstein equation and there’s a great example I found at https://demonstrations.wolfram.com/PumpJack/

There is one line to solve the Freudenstein equation for one of the angles:

Solve[0 == -b^2 + a^2 + c^2 + d^2 + 2 a c Cos[phi - alpha] - 
   2 a d Cos[phi] - 2 c d Cos[alpha], alpha]

However when I run it on my machine I have a problem:

  • It never solves. I have let it run for 24 hrs on my i7 machine and
    nothing is returned…no errors or solutions.
  • It only ever uses max 12% CPU.
  • It only ever uses 1GB or RAM on my 32 GB machine.

Question 1: Any tips on why this won’t solve? I can see a solution in the demonstration problem so the person who made the demo is clearly smarter than I.

Question 2: Is it normal for Mathematica 12.1 to only use limited CPU and memory?

Thank You

Freudenstein_Solve_Fail.nb (2.11 KB)

2

Probably the Demonstration was handling the case where those parameters {a,b,c,d,phi} were given explicit numeric values. Much easier to handle then.