Two grids, one rotating, share equivalent xy coordinates with different values.by Rlafrog Tags: axis of rotation, coordinates, grids, rotating 

#1
Apr412, 03:36 PM

P: 1

I’m a woodworker, a math idiot, my trig hasn’t improved since I flunked it 40 years ago and I need help making a Christmas toy for my grandkids. The values that follow are arbitrary, were extracted using eng graphics software and should be solid.
Problem: I have one 2D surface (that rotates) on a second 2D surface (that doesn’t rotate). It appears to me (?) that a given xy point on the rotating surface can be expressed using the xy coordinates of the nonrotating surface as a function of the degree of rotation –and also  where the axisof rotation of the (rotating) surface lives (on the nonrotating surface). Example: I have a piece of graph paper with an xy grid centered at (0,0) which I will call the Top Grid (T), and a point ‘p1’ drawn on the surface at T( 46.34, 41.69 ). I have a piece of plywood with a grid stenciled on the surface w/ a center at (0, 0) which I will call the Bottom Grid (B). I push a pin through the Top Grid at T(0,0) and pin it to the Bottom Grid’s point B(0,0) so that the Top Grid can rotate freely around the Bottom Grid’s centerpoint at (0,0). Stated differently, the axisofrotation for the Top Grid is point B(0, 0) on the Bottom Grid. I align the x and y axes of both grids (rotation = 0) and mark p1 (of the Top Grid) onto the bottom grid to find that: p1(x, y) = T(x, y) = B(x, y) = ( 46.34, 41.69 ), …no surprises. I rotate the Top Grid 10 degrees clockwise and mark p1 onto the Bottom Grid to discover that: p1(x, y) = T( 46.34, 41.69 ) = B( 52.87, 33.01 ) I separate the two grids so I can move the Top Grid’s axisofrotation to a different point on the Bottom Grid. Unfamiliar with Math terminology, any point on the Bottom Grid that serves as an axisof rotation for the Top Grid that is not ( 0, 0), I refer to as the Top Grid’s “xy offset”. I establish a new AoR for the Top Grid at B(46.45, 42.38) on the Bottom Grid. I align the axes of both grids (no rotation) and mark p1 onto the Bottom Grid to discover that: p1(x, y) = T( 46.34, 41.69 ) = B( 92.79, 0.6886 ) I rotate the Top Grid 8.5 degrees counterclockwise and mark p1 onto the Bottom Grid to discover that: p1(x, y) = T( 46.34, 41.69 ) = B( 86.12, 5.70 ) [I’m lousy at Mathspeak, but I’ll take a shot anyway …] Can someone help me with a formula that I can put into a spreadsheet that will give me the Bottom Grids xy equivalents for any xy point on the Top Grid as a function of the Top Grid’s AoR ‘x and y offset’ [from B( 0, 0) to B( x, y)] with an ndegree of rotation (of the (Top Grid)? 2. Relevant equations 3. The attempt at a solution I am attempting to solve this problem graphically, a technique that is not only prone to errors but extremely time consuming. Any help would be sincerely appreciated. 1. The problem statement, all variables and given/known data 2. Relevant equations 3. The attempt at a solution 



#2
Apr512, 01:13 PM

P: 41

The attached file shows an image from Excel that should work for you.



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