Understanding Basic Geometric Equations in Robotics Kinematics Analysis

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SUMMARY

The discussion focuses on the application of geometric equations in robotics kinematics analysis, specifically deriving the equation x2 = (a1^2 - a2^2 + x1^2)/(2 * x1) using the law of cosines. The variables defined include AC = a1, BC = a2, AB = x1, and AX = x2, with CX being perpendicular to AB. The user successfully solved the equation after initial confusion, demonstrating the importance of understanding geometric relationships in kinematics.

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  • Understanding of basic geometric principles
  • Familiarity with the law of cosines
  • Knowledge of robotics kinematics
  • Ability to interpret geometric diagrams
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Robotics engineers, students studying kinematics, and professionals involved in robotic design and analysis will benefit from this discussion.

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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)
 
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Don't bother. I was able to get it using the law of cosines.
 

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