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Rotational motion mechanism with quasi stops      


As seen on tv.

Having issues with animating the movement of two fielders, (25m apart on a straight line) when a baseball is struck towards them. they're on the y axis when they should be on the x.... and they should be green and brown dots, not lines.....

The mechanism of transport of the material of the sewing machine M 1022 class: mathematical animation. 

I have an equation for r(t) that involves 3 (slidable) constants; an equation for phi(t) that involves the same three constants and is written in terms of arctan; theta is a slidable constant. How do I plot this on an x,y,z plot? I want an animation in terms of t.

  One way to get rolling without slipping animation in 3d. The trajectory and circle are divided into segments of equal length. In the next segment of the trajectory we construct circle, taking into account the fact that it turned on one segment. Rolling sphere or cylinder can be simulated, if we take plottools templates of the same radius, and replace them on the site of our circle.

Spiral (equidistant) around the curve.  In this case, a spiral around the spiral.
So without any sense. 
If we re-save the animation with the program Easy GIF Animator, its size is reduced by about 10 times, and sometimes much more.

The method of solving underdetermined systems of equations, and universal method for calculating link mechanisms. It is based on the Draghilev’s method for solving systems of nonlinear equations. 
When calculating link mechanisms we can use geometrical relationships to produce their mathematical models without specifying the “input link”. The new method allows us to specify the “input link”, any link of mechanism.

Three-bar mechanism.  The system of equations linkages in this mechanism is as follows:

f1 := x1^2+(x2+1)^2+(x3-.5)^2-R^2;
f2 := x1-.5*x2+.5*x3;
f3 := (x1-x4)^2+(x2-x5)^2+(x3-x6)^2-19;
f4 := sin(x4)-x5;
f5 := sin(2*x4)-x6;

Coordinates green point x'i', i = 1..3, the coordinates of red point x'i', i = 4..6.
Set of x0'i', i = 1..6 searched arbitrarily, is the solution of the system of equations and is the initial point for the solution of the ODE system. The solution of ODE system is the solution of system of equations linkages for concrete assembly linkage.
Two texts of the program for one mechanism. In one case, the “input link” is the red-green, other case the “input link” is the green-blue.
After the calculation trajectories of points, we can always find the values of other variables for example the angles.
Animation displays the kinematics of the mechanism.

(if to use another color instead of color = "Niagara Dark Orchid", the version of Maple <17)


Can we get it in MapleSim, not in exactly this form, but in substance? (Not in Maple)
The line of intersection of surfaces:
(x1-0.5) ^ 4 + x2 ^ 4 + x 3 ^ 4-1. ^ 2 = 0.;
x1 ^ 2 + (x2-0.25) ^ 2 + x3 ^ 2-1. ^ 2 = 0.;
(Red) rotates about an axis oX3. During rotation, the line intersects with the fixed sphere ((0., 1.5, 0 .5); R = 1.725). One of the points of intersection is drawn in green. Green Dot and the center of the sphere connected to the blue segment.  In the sphere  of  fixed  trajectory of  the green point.
In other words, the geometric model  3d  cam mechanism and its kinematics.

Hi all,

I've got a parametric curve of the form f(x),h(x) x=0..1, and want to make an animation of this curve when changing an exogenous variable h0.

My attempt was to do it like this:

plots[animate](plot, [f(x), h(x), x = 0 .. 1], h0 = 0 .. 1)

but it doesn't work.

Does anyone know if/how this can be done?



Some Maple 18 short (and I believe elegant) code for doing gravitational simulations with N bodies in space:


Initial velocities have been tweaked to keep the system stable for the duration of the animation.


Please feel free to fiddle with its parameters, velocities and positions and/or N itself, to produce more interesting animations or re-use the code therein (You can safely ignore the (c), it's there just for archiving purposes).


The following are animations from three runs with N=4, N=3 and N=2, no other parameters changed.




Spiral on the cone. 

Yes, of course, in Maple.  The same source


Crosslinking surfaces by a spiral.

My fantasy is a source.

Has anyone solved this problem from an older Putnam paper?

An ellipse sitting in the first quadrant with its major axis parallel to the x axis is tangent to the positive x and y axes.

It slides clockwise within the first quadrant while maintaining tangency to both positive axes until its major axis is parallel to the y axis.

Prove that the locus of its centre is the arc of a circle.

I have crudely animated this motion by sliding the axes around the stationary ellipse. Is there a more elegant animation which slides the ellipse against stationary axes?

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