Complex geometries in mechanical engineering (updated)

When we say the word “complex” it doesn’t mean that the geometry is impossible to understand or to manufacture. Complex geometries are those hard to be understood from the first while (you can’t get the engineering reasons beyond this geometry immediately). In other words, drawings or schematics of complex geometries can’t express themselves, but you need someone to explain this geometry in few sentences.

The main complex designs comprise one the following layouts:

•   Helical shape with/without taper
•   2d or 3d spiral with/without taper
•   Twisted profile with/without taper

All of the previous layouts have a common reason which is continuous and smooth operation

1.      Complex rotor designs:

•   Progressive cavity pump
•  Radial flow pump impeller
•   Mixed flow centrifugal pump
•   Twisted-blade axial flow pump
•   Twisted-blade HAWT
•   Helical Savonius VAWT
•   Helical Darrieus VAWT
•   Twisted-blade gas turbine compressor
•   Twisted-blade gas/steam turbine (vortex blade)
•   Screw pump

2.      Complex gear designs:

•   Involute tooth shape
•   Helical gear
•   Worm gear
•   Bevel spiral gear

3.      Complex bearing designs:

•   Ball-screw bearing

4.      Complex power tools bits:

•   Twisted drill bit

Tricky side view

I was interviewed yesterday in a certain company, let's say "x". The interviewer (engineer) gave me a technical exam to solve. In fact I solved the whole exam except the following question: "given the following elevation and plan views draw the side view". It was frustrating not to solve the question because the views were very simple. My friend eng. M. Sayyed (working in this company) told me what the answer is.The answer was that explained in the next figure which shows the solved problem with the isometric view.

So, did you see ?!!

lately, I thought about those views and I figured out that there are another two possible isometric geometries that can produce the same elevation and plan views (see the following figure).

So, this problem gave me the anwer of my question : "can we create a software that can produce a third view from two given views?", now the answer is absolutely no.

Point inside convex hull test

Assume we want to check if a given point is inside a convex hull or not, we will do the following:

v  Divide the convex hull to triangles where all of these triangles have a common vertex which is arbitrarily chosen

v  Check if the point is inside one of the triangles. If the point is inside one of the triangles then it is inside the convex hull. Else if the point is not inside any triangle then it is out the convex hull.

The method used to detect if a point is inside a triangle looks like the following:

v  The prescribed triangle has three edges. For each edge create a triangle composed of the test point and an edge

v  Compute the area of the main triangle and the other three triangles. If the sum of areas of the constructed three triangles equals that area of the main triangle then the point is inside.

Note: I don’t know if this method is previously used or not, but what I know is that my mind gifted me this method.

World map with circles art work

I got the following image using "image processing and design toolbox" in Scilab environment to get the color of each pixel in the original image and drawing circles with random diameters. The color of each circle is the color of the pixel coincident with its center. Finally, I exported those circles to scalable vector graphics format which is easy to scale keeping the quality unchanged.

The code is time-consuming, so if I improved the code, I'll post it later. 

VAWT mounting layouts

Here you are two layouts for VAWT mounting and the required dimensions to be calculated for each layout. The rotor is drawn as a rectangle just for this schematic and the original rotor shape does not matter.

Spirograph

Spirograph is a geometric drawing toy that produces mathematical curves of the variety technically known as hypotrochoids and epitrochoids. The term has also been used to describe a variety of software applications that display similar curves, and applied to the class of curves that can be produced with the drawing equipment (so in this sense it may be regarded as a synonym of hypotrochoid). The name is a registered trademark of Hasbro, Inc.

The following figure shows the concept and geometric paraeters

The following are some curves drawn by the spirograph code I wrote in Scilab

Piston sealing modes for Stirling engine

Here you are the figure that explains what I want

Force meter with mechanical amplification

The amplification depends on the ratio between areas of pistons. Small force can produce large pointer displacement.

This force meter can work with both compression and tension forces. Also it can work as comparator

The spring here (in this design) will be compressed, but we can modify the design to make it elongating.

Low friction sealing is required for this device

Controlling dc motor speed using pc

Steps:

[]  Generate a sound wave of certain duration (in my case 10 seconds) with high frequency (say 20000 Hz) using my Scilab toolbox for tone generation.

[] Cut a wire from an old pc headphone including the TRS connector

[]  Connect one end of the dc motor with a diode and the other end of the diode with any wire out from the sound card.

[]  Connect the second wire with the motor

[]  Run the sound file with any media player and control the speed via volume control slider

Note: wave rectification is done by hardware (diode) and is not going to work when done by software

Note: when motor is connected without diode it is not going to rotate and it will behave as a speaker (you can hear songs from the motor!)

Graphical presentation of RGB 3d matrix

When I was using Image Processing and Design toolbox IDP 8.0 in Scilab environment I came over what's called "3d matrix". This 3d matrix is called RGB matrix also. Each pixel in any image requires to be defined 3 information: pixel row, pixel column, and the RGB values of this pixel. So, this matrix defines pixel location and color components. The size of this RGB matrix is M x N x 3 where M is image height in pixels, and N is image width in pixels.