Obtaining xy-coordinate linear motion from angles of rotation

In summary, the speaker is seeking help with calculating the rotation angles for two wedges in order to move a laser beam from one point to another within a 6cm radius circle. They have determined the relationship between the angles for the wedges and have a formula for "b", but are struggling with calculating it accurately for different coordinates. They are hoping for suggestions or assistance from someone who has experience with similar calculations.
  • #1
sk63
1
0
Hello,

I have a laser beam that passes through two 3 degree angled wedges, resulting in the ability to project the laser anywhere within a 6cm radius circle (each wedge alone produces a 3cm radius circle). I need to be able to tell each wedge how much to rotate in order to get the laser from one point (x1,y1) within that circle to another point (x2,y2), and can’t seem to get the formula for the rotation angles correct…

I have determined that the angles for the two wedges will have the following relationship:
ThetaWedge1= arctan(y/x) + b
ThetaWedge2 = arctan(y/x) – b

Where “b” is a function of x and y. and 2b=ThetaWedge1-ThetaWedge2

The equation for “b” is what I am having trouble calculating and have been getting results that produce correct angles of rotation for some (x,y) coordinates and incorrect ones for others.

(Note: this equation form is just for the first quadrant, for other quadrants there will be another factor to take the quadrant into account)

This will be in a Matlab loop, so it can be assumed that each (x2,y2) point will become the (x1,y1) point for the next movement/ set of rotations.

If anyone has any ideas or has done calculations similar to these in the past, you help is much appreciated! Thanks!
 
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  • #2
sk63 said:
The equation for “b” is what I am having trouble calculating and have been getting results that produce correct angles of rotation for some (x,y) coordinates and incorrect ones for others.

(Note: this equation form is just for the first quadrant, for other quadrants there will be another factor to take the quadrant into account)
It would help to have a picture or at least the other formulas, too. Otherwise you can still solve for ##b## in each quadrant.
 

FAQ: Obtaining xy-coordinate linear motion from angles of rotation

How can angles of rotation be converted into xy-coordinate linear motion?

Angles of rotation can be converted into xy-coordinate linear motion through the use of trigonometry. By using the sine and cosine functions, the x and y coordinates of a point can be calculated based on the angle of rotation and the length of the line segment.

What is the relationship between angle of rotation and xy-coordinate linear motion?

The angle of rotation and xy-coordinate linear motion have a direct relationship. As the angle of rotation increases, the linear motion in the x and y directions also increases. Similarly, as the angle of rotation decreases, the linear motion decreases as well.

Can angles of rotation be used to control the precise linear motion of an object?

Yes, angles of rotation can be used to control the precise linear motion of an object. By accurately calculating the x and y coordinates based on the angle of rotation, the object can be moved to a specific location with precision.

How can the accuracy of converting angles of rotation to xy-coordinate linear motion be improved?

The accuracy of converting angles of rotation to xy-coordinate linear motion can be improved by using more precise measuring tools and advanced mathematical techniques. Additionally, reducing any sources of error, such as friction, can also improve the accuracy of the conversion.

Are there any limitations to obtaining xy-coordinate linear motion from angles of rotation?

Yes, there are some limitations to obtaining xy-coordinate linear motion from angles of rotation. The accuracy of the conversion may be affected by external factors such as friction, air resistance, and the surface on which the object is moving. Additionally, the conversion may not be as accurate for complex shapes or curves.

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