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Post by yardstick on Aug 29, 2017 22:18:29 GMT -6
(Continued) So we have this crank-slider, and we want to analyze it, so that we can demonstrate multi-dimensionality. We have established there are angles and arm lengths, and to do some analysis, we want to keep things as simple as possible, so the easiest way to do that is to evaluate the crank-slider mechanism when it is at its extreme left position and its extreme right position. Here are some sketches:  This is the extreme right position of the mechanism. You can see the arms are both extended to the furthest point on the right. When the mechanism is in this position some things stand out: r 1 = r 2+r 3θ 1 = 0° θ 2 = θ 3θ 3 = 180°  This is the extreme left position of the mechanism. You can see that the arms overlap each other to make the block go as far left as possible. When the mechanism is in this position some things stand out: r 1 = r 3-r 2θ 1 = 0° θ 2 = 180° θ 3 = θ 1Well, what about when the mechanism is in the middle, between the ELP and ERP? Lets set the mechanism such that the angles will be easy to work with:  Look at what we did here: We set the angle between r 2 and r 3 equal to 90°. Why did we do that? Because then we have a 90° angle in the triangle r 1 - r 2 - r 3, and we can use trig functions and pythagorean theorem with impunity! And it simplifies the problem. Now we have: r 12 = r 22 +r 32 and if we let θ 2 be our angle of interest we have: sin θ 2 = r 3/r 1tan θ 2 = r 3/r 2cos θ 2 = r 2/r 1
(continued...) |
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Post by yardstick on Aug 29, 2017 23:25:15 GMT -6
(continued)
Alright, we have now several equations to work with, but we need to do some reorganizing...
sin θ2 = r3/r1 ---->> r3 = r1sinθ2
tan θ2 = r3/r2 ----->> r3 = r2tanθ2
cos θ2 = r2/r1 ----->> r2 = r1cosθ2
and r12 = r22 + r32
and we know that r1, θ2 and θ3 are variable, and r2, r3 and θ1 are fixed (constants). We also know by observation, that θ3 and r1 are dependent upon the angle θ2 because θ2 is the crank!
So θ2 is the independent variable, and θ3 and r1 are the dependent variables!
What we have just done is called position analysis. When the fixed values are known, we can determine the variables. That is, when the independent variables are known, we can calculate the dependent variables. In english: When we know what the crank angle (θ2)and length (r2) is, the linkage length (r3), and the slider angle (θ3), we can calculate the linkage angle and slider position for any known angle of the crank.
(continued...)
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Post by whatif on Aug 30, 2017 10:37:04 GMT -6
Yaaayyy, yardstick! I was hoping you'd continue the math thread!
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Post by Rick on Aug 30, 2017 11:12:38 GMT -6
Hello and props to everyone in this thread. My name is Rick and by no means do I want to hijack this thread. I just wanted to introduce myself and tell yardstick what a great job he is doing.
I am not an intelligent person nor do I speak or write intelligently. I must admit, even though I received a degree in Aero-Space Theory and applied Sciences and was required to take Trig (that was a couple lifetimes ago) yardstick has managed to lose me.
I have been a long time follower of Dr. Chuck Missler (20+ yrs) and he seems to be the most intelligent person I have ever encountered.
Even though I do not speak or write intelligently my comprehension of those that do far exceeds my ability to do so.
My question for yardstick, how does Quantum theory (String Theory) or Quantum Mechanics tie into this?
It's very nice to meet (insert accent) y'all and I look forward to further discussions.
God Bless~
2Ti 2:15 KJV
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Post by yardstick on Aug 30, 2017 11:35:29 GMT -6
Hello and props to everyone in this thread. My name is Rick and by no means do I want to hijack this thread. I just wanted to introduce myself and tell yardstick what a great job he is doing. I am not an intelligent person nor do I speak or write intelligently. I must admit, even though I received a degree in Aero-Space Theory and applied Sciences and was required to take Trig (that was a couple lifetimes ago) yardstick has managed to lose me. I have been a long time follower of Dr. Chuck Missler (20+ yrs) and he seems to be the most intelligent person I have ever encountered. Even though I do not speak or write intelligently my comprehension of those that do far exceeds my ability to do so. My question for yardstick, how does Quantum theory (String Theory) or Quantum Mechanics tie into this? It's very nice to meet (insert accent) y'all and I look forward to further discussions. God Bless~ 2Ti 2:15 KJV I am not sure. I graduated with my second bachelors a year or so ago (Mechanical Engineering), and was introduced and had a lot of work in physics and math (a little chem too). I formulated a hypothesis that imaginary numbers are what allow us to comprehend and mathematically model 4+ dimensional math. (Time is a gravitational effect, although we use it in math and physics because we have no 4D representations we can use - they are not accessible in a 3D universe). The third course in college level calculus involves using parametric equations, but only uses a single variable as the parameter (typically t for time). For dimensions greater than 4D, we would have to have additional parameters to do this calculus with. It gets stupid complicated going beyond 1 parameter. In another thread we had a discussion related to the nature of God and that he was a multidimensional being. I suggested there that it was possible to demonstrate 4+ dimensional math, and (I believe) that I did up to 7 dimensional math in school. The messages in this thread related to i = -i was a proof that the 5th-7th dimensions are spatially the same as the 8th-10th dimensions in 3D mathematical modelling (I believe this may be related to the Heisenberg Uncertainty Principle). By spatially, I mean, that they occupy the same 'space' because their features have magnitudes and locations that are the same (i = -i). We had a brief interlude about hypercubes, and how they demonstrate that we can only model 4+ dimensions mathematically in 3D (we cant actually build them), because of the limitations of a 3D universe. We cannot build physical models of 4D+ objects, we can only build up to 3D projections of them. Hope this helps |
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Post by watchmanjim on Aug 30, 2017 13:23:56 GMT -6
. . . for now we see through a glass [very] darkly. . . .
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Post by yardstick on Sept 22, 2017 9:30:40 GMT -6
(Continued) So we have this crank-slider, and we want to analyze it, so that we can demonstrate multi-dimensionality. We have established there are angles and arm lengths, and to do some analysis, we want to keep things as simple as possible, so the easiest way to do that is to evaluate the crank-slider mechanism when it is at its extreme left position and its extreme right position. Here are some sketches: This is the extreme right position of the mechanism. You can see the arms are both extended to the furthest point on the right. When the mechanism is in this position some things stand out: r 1 = r 2+r 3θ 1 = 0° θ 2 = θ 3θ 3 = 180° This is the extreme left position of the mechanism. You can see that the arms overlap each other to make the block go as far left as possible. When the mechanism is in this position some things stand out: r 1 = r 3-r 2θ 1 = 0° θ 2 = 180° θ 3 = θ 1Well, what about when the mechanism is in the middle, between the ELP and ERP? Lets set the mechanism such that the angles will be easy to work with: Look at what we did here: We set the angle between r 2 and r 3 equal to 90°. Why did we do that? Because then we have a 90° angle in the triangle r 1 - r 2 - r 3, and we can use trig functions and pythagorean theorem with impunity! And it simplifies the problem. Now we have: r 12 = r 22 +r 32 and if we let θ 2 be our angle of interest we have: sin θ 2 = r 3/r 1tan θ 2 = r 3/r 2cos θ 2 = r 2/r 1
(continued...) I hit the reply button to make this post so that the pics above would be available; but it looks like it didnt work. If we take the derivative of the formulas we developed above, we can determine the velocities of the moving parts. The derivatives would be taken with respect to θ, if memory serves. Taking a second derivative gives the instantaneous acceleration of each of the moving parts. The second derivative would also be with respect to θ. The 5th-7th dimensional stuff comes in when we design the arms for the crank and slider. If one of the arms is too short, the slider block will strike the crank. if too long, the slider block will strike the end of the channel it is sliding in. This is represented in the derivatives with the values of cosine θ or sine θ (found in the denominator of the formula) being equal to 0. Alternately, this is found when the formula, which has a radical over part of it, is evaluated to be the square root of a negative number (usually -1). Whenever there is the square root of a negative number you are dealing with imaginary numbers. Plotting a number coordinate for X and Y on a 'real' axis does not consider the imaginary part of the equation. In fact DeMoivre's Theorem indicates that in a linear equation, there can be both a real part, and an imaginary part. The imaginary part is plotted on the 'y' axis, although its really the imaginary part of the X axis, or imaginary part of the Y axis, depending on what variables you use. When taken from Euler's formula e iθ = cos θ + i sin θ, De Moivre's is basically the same, except you have a constant n: e inθ = cos nθ + i sin nθ cos nθ and i sin nθ wind up being the roots of the derivation when the quadratic formula is applied: x = b +/- sqrt(b 2 - 4ac) This is where you get the imaginary part of De Moivre's/Euler's formula, as previously shown. The imaginary part, which is plotted on the imaginary part of the X or Y axis 'splits' the X and Y axes into two axes, real and imaginary, making 3 more dimensions: X - real Y - real Z - real t - time X - imaginary Y - imaginary Z- imaginary 7 dimensions. Since we have previously proven that i = -i, that gives us 3 more dimensions, for a total of 10. X - real Y - real Z - real t - time X - imaginary i Y - imaginary i Z- imaginary i X - imaginary -i Y - imaginary -i Z - imaginary -i 10 dimensional math. QED Oh yeah, your real life application of a crank-slider: The pistons on your car engine. |
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Post by whatif on Sept 22, 2017 22:51:25 GMT -6
Glad to see more in this thread, yardstick! Way cool!
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Post by yardstick on Sept 22, 2017 23:07:33 GMT -6
Glad to see more in this thread, yardstick! Way cool! Sorry that the last post is lacking in a little content. I was kinda in a hurry to get it done. All things considered... I can try to flesh it out if we are all here past tomorrow. |
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Post by anonymouse on Sept 23, 2017 7:46:59 GMT -6
Im lost, this is such high level math. Is this what you guys use in engineering?
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Post by yardstick on Sept 23, 2017 10:10:44 GMT -6
Im lost, this is such high level math. Is this what you guys use in engineering? The last couple posts are used in robotics and where any movement of (for example) an arm might need to have a mathematical model to demonstrate that it will move correctly before being programmed, or built. A very common use is in the creation of the piston arms and joints in a car engine. One does not want the piston head to hit the valve cover. |
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Post by mike on Sept 23, 2017 10:20:10 GMT -6
Im lost, this is such high level math. Is this what you guys use in engineering? The last couple posts are used in robotics and where any movement of (for example) an arm might need to have a mathematical model to demonstrate that it will move correctly before being programmed, or built. A very common use is in the creation of the piston arms and joints in a car engine. One does not want the piston head to hit the valve cover. Don't want the Piston to hit the cylinder head, not the valve cover. As a gear head I'm just being picky  |
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Post by linda on Sept 23, 2017 10:53:35 GMT -6
Being new here, I've just skimmed through this whole thread for the first time. I took college calculus a few decades ago (won't say how many), so some of the math is familiar. But I want to ask a question about something that jumped out at me way back at the beginning - about fallen angels being more than 3 dimensional, so they can always find us. Now that's something I've never thought about, and I'm wondering why you would think that? They were created, like we were. So how do we know that?
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Post by yardstick on Sept 23, 2017 11:25:06 GMT -6
Being new here, I've just skimmed through this whole thread for the first time. I took college calculus a few decades ago (won't say how many), so some of the math is familiar. But I want to ask a question about something that jumped out at me way back at the beginning - about fallen angels being more than 3 dimensional, so they can always find us. Now that's something I've never thought about, and I'm wondering why you would think that? They were created, like we were. So how do we know that? The theory is that since they do not have capacity for dominion, there must be something different about them. Hypotheses fall into three categories (so far): 1. Genetics - this explains the Nephilim/Angel theory of Genesis 6, and Jude 1:6, and that they are 'created beings' like Adam (but not like the rest of humanity); 2. The dimensions allotted to them are not the same 3 dimensions given to mankind, though there is some overlap - namely they have to be at least 4-dimensional beings to be able to come and go from the 3-dimensional world of men. There is a lot of anecdotal evidence for this, namely, the 'appearing' and disappearing from in front of individuals. 3. A combination of both 1 and 2. The 'math class' is simply to demonstrate that while we cannot create 3-D models of 4+ dimensional objects, we can mathematically calculate and formulate them, up to 10 dimensions. Incidentally, three things: 1. The 4th dimension, which is not time (a property of gravity) - I have not been able to figure out mathematically what it is. But it would make a lot of sense if the Angels were 4th dimensional beings. 2. 5th-7th dimensional beings could be in two places at the same time - real and 'imaginary' (+ i) 3. 8th-10th dimensional beings could be in 3 places at once, + i, - i (see the proof) and real |
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Post by yardstick on Sept 23, 2017 11:38:47 GMT -6
The last couple posts are used in robotics and where any movement of (for example) an arm might need to have a mathematical model to demonstrate that it will move correctly before being programmed, or built. A very common use is in the creation of the piston arms and joints in a car engine. One does not want the piston head to hit the valve cover. Don't want the Piston to hit the cylinder head, not the valve cover. As a gear head I'm just being picky Thanks mike! I have the theory, not the practical application! |
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This is the extreme left position of the mechanism. You can see that the arms overlap each other to make the block go as far left as possible.
Look at what we did here: We set the angle between r2 and r3 equal to 90°. Why did we do that?
