1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Complex number method for kinematic equations

  1. Jun 6, 2012 #1
    1. The problem statement, all variables and given/known data
    Objective:
    1. For a two-arm manipulator, use complex-number method to derive the displacement, velocity and acceleration equations for the tracing point P.
    2. For a two-arm manipulator, use complex-number method to derive the displacement, velocity and acceleration equations for the center of gravity for each arm assuming it is located halfway between the joints.
    3. Construction graphical solutions for 3 positions.



    2. Relevant equations
    The arm lengths are 1" each. angular velocity: ω=1rad/s, angular acceleration: α=1rad/s^2



    3. The attempt at a solution

    I get a little lost in the algebra.
    So far I have a*e^(i*theta) + b*e^(i*phi) = x + i*y

    I separated into real and imaginary:

    Real: a*cos(theta)+b*cos(theta)=x

    After dividing by i...I get:

    Imaginary: a*(sin(phi)) +b*sin(phi) = y

    Then I'm not sure what to do.

    Thanks,

    -D

    p.s. If anyone knows how to model this in either matlab or excel...please email me!
     

    Attached Files:

    Last edited: Jun 6, 2012
  2. jcsd
  3. Jun 13, 2012 #2

    BruceW

    User Avatar
    Homework Helper

    It's not quite right. for the real part, you've written theta in both cosines, but that's not right, if you think of the trigonometric form of a complex number. (And you've got a similar mistake for the imaginary part). Maybe write out the complex numbers explicitly in trigonometric form, instead of skipping this step.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Complex number method for kinematic equations
Loading...