Understanding Basic Geometric Equations in Robotics Kinematics Analysis

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In summary, geometry is a branch of mathematics that deals with the properties, relationships, and measurements of points, lines, shapes, and solids in space. The basic concepts of geometry include points, lines, angles, planes, and shapes such as circles, triangles, and rectangles. 2D geometry deals with shapes and figures in a two-dimensional plane, while 3D geometry deals with objects in three-dimensional space. To calculate the perimeter of a shape, one must add the lengths of all its sides. The Pythagorean Theorem states that in a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the other two sides. It can be written as a² + b²
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phiby
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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.
 

1. What is geometry?

Geometry is a branch of mathematics that deals with the properties, relationships, and measurements of points, lines, shapes, and solids in space.

2. What are the basic concepts of geometry?

The basic concepts of geometry include points, lines, angles, planes, and shapes such as circles, triangles, and rectangles.

3. What is the difference between 2D and 3D geometry?

2D geometry deals with shapes and figures in a two-dimensional plane, while 3D geometry deals with objects in three-dimensional space.

4. How do you calculate the perimeter of a shape?

The perimeter of a shape is the distance around its outer edge. To calculate it, you need to add the lengths of all the sides of the shape.

5. What is the Pythagorean Theorem?

The Pythagorean Theorem states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides. It can be written as a² + b² = c², where c is the length of the hypotenuse and a and b are the lengths of the other two sides.

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