Understanding Basic Geometric Equations in Robotics Kinematics Analysis

  • Thread starter Thread starter phiby
  • Start date Start date
  • Tags Tags
    Geometry
phiby
Messages
74
Reaction score
0
http://www.flickr.com/photos/66943862@N06/6868453382/in/photostream/lightbox/
http://www.flickr.com/photos/66943862@N06/6868453382/in/photostream/lightbox/


I was looking at a robotics kinematics analysis & there is one geometric equation assumed in the analysis which I can't seem to understand. I have a simplified diagram above.

In the above diagram
AC = a1
BC = a2
AB = x1
AX = x2

CX is perpendicular to AB

From here, how does one get to
x2 = (a1^2 - a2^2 + x1^2)/(2 * x1)
 
Last edited by a moderator:
Mathematics news on Phys.org
Don't bother. I was able to get it using the law of cosines.
 
Insights auto threads is broken atm, so I'm manually creating these for new Insight articles. In Dirac’s Principles of Quantum Mechanics published in 1930 he introduced a “convenient notation” he referred to as a “delta function” which he treated as a continuum analog to the discrete Kronecker delta. The Kronecker delta is simply the indexed components of the identity operator in matrix algebra Source: https://www.physicsforums.com/insights/what-exactly-is-diracs-delta-function/ by...
Fermat's Last Theorem has long been one of the most famous mathematical problems, and is now one of the most famous theorems. It simply states that the equation $$ a^n+b^n=c^n $$ has no solutions with positive integers if ##n>2.## It was named after Pierre de Fermat (1607-1665). The problem itself stems from the book Arithmetica by Diophantus of Alexandria. It gained popularity because Fermat noted in his copy "Cubum autem in duos cubos, aut quadratoquadratum in duos quadratoquadratos, et...
Thread 'Imaginary Pythagorus'
I posted this in the Lame Math thread, but it's got me thinking. Is there any validity to this? Or is it really just a mathematical trick? Naively, I see that i2 + plus 12 does equal zero2. But does this have a meaning? I know one can treat the imaginary number line as just another axis like the reals, but does that mean this does represent a triangle in the complex plane with a hypotenuse of length zero? Ibix offered a rendering of the diagram using what I assume is matrix* notation...
Back
Top