I have my equation as a function of time which will take the value in radians here.
See my geometry attachment.
I would like to use the equations (Solidworks function with variables that will take my initial data)
Here is my parameterization on the two parameterized equations
X = (R*cos(t))-(Rr*cos(t+arctan(sin((1-N)*t)/((R/EN)-cos((1-N)*t)))))-(E*cos(N*t)) Y = (-R*sin(t))+(Rr*sin(t+arctan(sin((1-N)*t)/((R/EN)-cos((1-N)*t)))))+(E*sin(N*t))
Parameterization of the equation as a function of t.
R=10, E=0.75, Rr=1.5, N=10 my test base.
=(10*cos(t))-(1.5*cos(t+arctan(sin((1-10)*t)/((10/0.75*10)-cos((1-10)*t)))))-(0.75*cos(10*t)) by overriding the parameters.
the valid geometric profile is generated well, my question is it possible in a parameterized equation to put parameters inside, I can do it in a normal sketch by entering the parameters defined in the Equation table in the tools menu (Sigma).
But my problem is that I don't have a conversational way to nest a definition by variables in a parameterized equation, I'm stuck, I have to go through a calculation and replace my parameters with the values.
In the formula, limits exist when I am outside the definition domain of one of the sub-functions, but it is manageable;
The expected result exists and I can send my file in CAD/CAM to make a reducer based on cycloid(s) out of phase by 180 °, i.e. ft.
It remains to determine the energies and the known pressure losses or stresses imposed by the functional specifications, and a fatigue study to evaluate the lifespan of the various parts. This is the beginning of a project to have alternatives to make high-reduction robotics elements with high torques, my base 50 N.M bearing 6202.
Thank you for your request, I hope it's clearer............. Not easy to translate but I have no solution to make iterations, my goal is to do a parametric study with the use of simulation first in static to trigger a harvest of values and obtain relevant criteria on the increase of contact areas based on a non-matting condition.
Quote: "I don't have a conversational to nest a definition by variables in a parameterized equation"
If your question is about the possibility of using variables for the creation of a parametric sketch spline, I see two possible answers:
- directly in the "Equation-driven curve" sketch feature, after defining the variables (R, Rr, e, and Nl) in the [Equations] folder of the SolidWorks tree. You simply have to put the variables in quotation marks in the expressions of the coordinates: ("R"*cos(t))-("Rr"*cos(t+arctan(sin((1-"Nl")*t)/(("R"/"e"/"Nl")-cos((1-"Nl")*t)))))-("e"*cos("Nl"*t)) (-"R"*sin(t))+("Rr"*sin(t+arctan(sin((1-"Nl")*t)/(("R"/"e"/"Nl")-cos((1-"Nl")*t)))))+("e"*sin("Nl"*t))
It's perfect, the first solution corresponds 100% to our needs.
Thank you for the time spent saving me a hassle to calculate the different tests, now we change the desired value in the identified variable as for a more basic parameterization.
Have a good week to you.
Spectrum.
P.S:
Tomorrow I will resume the analysis with this time the search for an optimized thickness for the cycloid part with the simulation module.
Before doing the machining phase, I would like to be able to get the trajectory of the cycloid that would go through the 9 pins. (10 ........... mistake );
The goal is to have a continuity of the profile complementary to the formed base cycloid.
I do not quite see the meaning of your two expressions: - "trajectory of the cycloid that would pass through the 9 pins" and - "Complementary profile to the formed basic cycloid".
In a cyclo-type gearbox, there is in principle one more gauge than lobes on the cam. In your case, 9 lobes so 10 piges. With an adapted repetition (10 occurrences, the center of the circle on the right point of the eccentration and the pins arranged symmetrically with respect to a horizontal axis), the 10 pins are tangent to the cam profile. Was that the meaning of your question?
What do you want to achieve: - the equations of the envelope curves of the freelancho? The equation of the trajectory of its center? - images of these same curves built with SolidWorks sketching functions (if possible)?
In the first case, you should at least give the kinematics that allowed you to define the parametric equations of your initial curve, which is one of the envelopes of the gauge. Obviously, it is initially two circles that roll without sliding over each other. But then...? How exactly are your different parameters defined? A diagram would be welcome...
I have all the elements, in fact the goal is to allow more torque to be transmitted than when using a gear(s) transmission;
the contacts are more numerous with the use of a cycloid and picks, but in a second step why not replace the picks by the shape generated by all these picks but with the value of the eccentric;
To give you a precise idea, a very efficient simulator is present on this site and by analyzing the source code I have all the information requested for the cycloid but not to have the equation of the envelope generated by these freelancers, I have exchanged with colleagues in my office and we are stuck on this complementary part. By construction it is achievable but basically one person in our group wanted the equivalent to the first parameterized equation, no obligation to go through this path.
It is a variant of the first parameterized equation approach.
Here is the commented source code of the cycloid plot:
D = large diameter d = small diameter N = pin number E = eccentricity value
R = Q / 2 r = d / 2
// Mandatory constraints: // 3 < N < 50 // e < d/2 // r < R * Math.sin( Math.PI / N )
// To draw a epitrachoid, we need r1 (big circle), r2 (small rolling circle) and d (displament of point) // r1 + r2 = R = D/2 // r1/r2 = (N-1) // From the above equations: r1 = (N - 1) * R/N, r2 = R/N
r1 = (N - 1)* D / 2 / N r2 = D / 2 / N
// Parametric equation: X = (r1 + r2) * cos(2 * pi * u) + e * cos((r1 + r2) * 2 * pi * u / r2) Y = (r1 + r2) * sin(2 * pi * u) + e * sin((r1 + r2) * 2 * pi * u / r2)
// For u varying from 0 to 1
We use these equations to generate a daisy "easily" with something like this (but I don't take into account eccentricity):
One last contribution... I still haven't fully grasped your questions. In a traditional Cyclo gearbox, the pins are in contact with the lobe cam, the outer surface of which forms the envelope of these cylindrical pins. Your initial parametric equations are those of this envelope. To obtain the trajectory of the center of the picks, we just have to replace Rr by 0 in these equations. In the attached zip file, I offer you a document that indicates how these equations are established, and an Excel file that illustrates them.
What escapes me is your sentence: "why not replace the piges by the form generated by all these pigs but with the value of the eccentric" Would it be a question of finding the conjugate surface of the cam profile in its movement with respect to the frame, i.e. its envelope, as in the illustration below? If so, the matter becomes terribly complicated... Note that the version with pits is theoretically hyperstatic (if you are looking for the simultaneous contact of several pins) and requires precise machining and assembly. A version with conjugated profiles will be worse...
Thank you for all the explanations and the creation of the EXCEL table.
Your illustration is beautiful and corresponds well to this famous counter-form.........
For the moment it is a development (under study) to make a gearbox as compact as possible with this process.
Mastering machining will pose difficulties.
Originally, the question was asked by a colleague present on this project (there are only two of us........) "if we used the envelope generated by the gauges" and it is a conjugate surface.
I have just gone through your documents and I thank you for the explanations and the Excel file which integrates the original formula.
For me, I have the elements to make a model and start printing the prototype.
I will take the time to take up and assimilate your work, I very much appreciate the richness of this forum which allows us to progress.
I will submit a model soon to illustrate this work. Have a nice weekend.
P.S:
I understand for the hyperstatic phenomenon, and in reality we are planning to buy an NC machine that will allow us to have finer tolerances. The approach is done in plastic printing and then switching to an alloy to have suitable characteristics.
A week, and a few thoughts later... Contrary to what I imagined, the definition of the conjugate surface of the cyclo's cam-rotor is not out of reach. All it takes is a little vector calculation, and the profile can be defined point by point, so it can be easily integrated into SolidWorks in the form of a "curve passing through XYZ points". Everything is in the attached zip that replaces and completes my previous shipment.
One remark, however: this solution with direct contact with surfaces may appear to be more efficient than the one with pickets because of maximized contact radii, and therefore a reduced Hertz pressure. On the other hand, it cannot free itself from sliding friction, hence a degraded performance. Unlike the solution with the pins, which can be equipped with roller bearings (subject to a sufficient diameter).
Another point: the multiple contacts between cam and frame induce a high hyperstaticity, whatever the solution chosen. The version with direct cam/frame contacts gives the parts a high stiffness, combined with delicate machining. It will be difficult to control and distribute the forces at the cam/frame contacts. This hyperstatic character could be less critical with pins/rollers with a simpler geometry, and lower stiffness.
I have just opened the result of your work. We thank you for this achievement with our constraints of modeling by equation which were basically a misconception (integral counterform without integrating all the problems generated.......... It's a compromise to have, so the realization will be double to observe after different cycles the wear after a break-in, it's research for the moment, the purpose is to have compact gearboxes to integrate / and create pivotal links to reproduce a mechanism on a part of a robot.
A large part of adjustment and machining to be expected in all cases.
The use of rotating parts on the pickets allows for a more controlled realization, to be seen after the installation of the elements, but with
A second life also with the possibility of changing elements, in our monobloc idea not the possibility of compensating for wear and tear.
The first prototypes will be printed and the functional surfaces will be retouched in completion.
Not the necessary precision at the exit of the machine.
Introducing printed elements is a desire on difficult geometries, in CAD/CAM with the equations the machining of this gearbox is possible without going through printing which poses difficulties on the orientation of the wires and cross layers except by the PA12 polymer powders HP machine but with characteristics associated with this material. In metal printing, there is a problem of heat diffusion and deformation with the residual tensions after breakage of certain printing-related supports, doing post-processing but integrating everything into the source 3D model of the part requires a lot of iterations and the most constant wall possible.
Have a nice day, thank you for the time devoted to our request and the working documents.
