Comments on: Low Cost Accurate 3D Positioning

By: Sumit Aich

Sumit Aich — Thu, 01 Mar 2018 04:26:15 +0000

You MUST have maximum surface area of contact between aluminum foil and water.

the reason is that the current density vector must be normal to the end planes at all points on the plane. This can only be made possible if the ENTIRE end plane is an equipotential surface. Since aluminum has negligible resistivity compared to water, it acts as an equipotential surface and must cover the entire end planes.

By: Sumit Aich

Sumit Aich — Thu, 01 Mar 2018 04:25:39 +0000

If u wanna map an object, u must attach a 3D version of the Jefferson polygraph to the stylus.

https://en.m.wikipedia.org/wiki/Polygraph_(duplicating_device)

By: Sumit Aich

Sumit Aich — Thu, 01 Mar 2018 04:25:17 +0000

solid non-conductive or conductive objects (other than stylus) must NOT be submerged into the water because –

In simple terms – The voltage won’t drop linearly with displacement. So the water potentiometer principle won’t work.

In not-so-simple terms – Due to solid non-conductive objects submerged in water, the area of cross-section of water (above the submerged object) will decrease, so the magnitude of current density (dI/dA) vector will increase, so the magnitude of potential gradient / electric field intensity (J x p) vector will not be constant with respect to horizontal position. Thus, first derivative (dV/dx) of output voltage with respect to position will not be constant. In other words, the “output voltage will NOT be directly proportional to horizontal position”. This violates the basic principle of a potentiometer.

By: Sumit Aich

Sumit Aich — Thu, 01 Mar 2018 04:24:50 +0000

Many people are confused regarding the use of slant electrodes instead of perpendicular electrodes in my 3D sensor. Well, here’s the deal.
In case of cuboid, the normal vector to the 3 planes will be parallel to the horizontal base. So the angle between normal vector and z-axis equals pi/2 radians. So the ‘n’ direction cosine of normal vector equals 0. So the 3rd column of the matrix of direction cosines of the 3 planes is a column of 0s . The determinant of a matrix is 0 if any of its rows or columns are 0. So matrix ‘A’ is a singular matrix. For a non-homogeneous system of 3 unknowns, if matrix ‘A’ is singular, it implies that the system of equations will have either no solution or infinity number of solutions.Since, 3rd column of matrix is 0, so its matrix of co-factors is a null matrix. Transpose of a null matrix is a null matrix. So adj(A) is a null matrix. So (adj(A)).B is also a null matrix. This will prove that the system of equations is consistent and has infinity number of solutions. This issue is not present in case of slant electrodes.

By: Sumit Aich

Sumit Aich — Thu, 01 Mar 2018 04:23:34 +0000

If you face any issues while reconstructing this water-based 3D sensor, feel free to ask here