In Electromechanical Displays, Part 1: The Nipkow Disk, the Nipkow disk was considered as a possible low-cost, mechanically-simple, perspicuous display like that of oscilloscopes. The Nipkow disk geometry was worked out in some detail and it is unattractive. The search for a better scheme continues in this second part.
A variation on the Nipkow disk is the “Nipkow drum”, made by spinning a steel can such as the one shown for New Zealand butter. It has a radius of R = 5 cm and a useable height of 6 cm. A spinning drum has the advantage over a Nipkow disk of linear rather than rotational motion in the horizontal dimension. The curvature of the can must still be corrected like that of a CRT with a curved screen. This is a lesser problem than nonlinearity in both dimensions of the screen. The disadvantage over the disk is that spinning a can is somewhat more mechanically involved than spinning a disk, but not by much. The most difficult task is to center the motor shaft at the center of the can to avoid wobble in its rotation. While various kinds of motors could be used, readily available, low-cost motors are spindle motors from hard disk-drives. These motors are nearly ideal for the application because they are designed to spin platters similar to the can, as shown below.
The screen dimensions of a Tek 454 oscilloscope are 0.8 cm/div or Y = 6.4 cm and X = 8 cm. For the butter can,
The arc angle swept out for the display is
and has 0.75 cm/div, slightly smaller than the 454 screen. The angle is less than for the disk because of the distance-amplifying effect of curvature projection. The line spacing at a resolution of 10 lines/div is 0.75 mm. The pixel holes in the can should be 0.75 mm in diameter, or about 30 mils, corresponding to a 28 mil # 70 drill bit.
A mechanical sketch of the Nipkow drum assembly is shown below. The display circuit board is floated above (and envelops) the spinning can with four corner standoffs, and is cabled to the motor-drive board below it. A LED board is suspended into the can from the display board, as shown. Only the can and motor shaft rotate. Each LED is optically separated by baffles and each illuminates one of N sectors of lines. By processing N sets of lines concurrently, the same line limitation that applies to Nipkow disks is remediated.
Curvature correction for the x -axis caused by the can curvature is similar to that for curved-screen CRTs. The geometry is shown below.
The distance from the tangential intersection at mid-screen of the x and x ’ axes along the curved (x ’) axis is
x’(θ) = R·θ
Along the flat-screen projection that is the x axis, the corresponding point is at
Solving for the angle, θ , that the two axes share in common,
Curvature correction requires that pixel holes placed along the x ’ axis be placed at intervals that correspond to regular (equally-spaced) intervals along the x -axis. The locations along the circumference of the can correspond to the linear screen projections as
The two axes are plotted below as a function of x . At x = 5 cm, θ = 1 radian and the projected x is about 5/4 = 1.25 larger than x ’. Thus, for a point on the flat screen at 5 cm, the corresponding hole in the can must be drilled at about 4 cm from the center of the screen. The curvature of the can nonlinearly “amplifies” the projected position of pixels viewed on a linear axis.
From the correction equation, a template can be plotted in a math program (such as Mathcad, from which the above plot was taken) and printed, with holes at the correct locations for a linear display. The paper template is wrapped around the can and a center-punch applied to the hole locations.
An additional line with one or more holes can be used with an optical interrupter to synchronize the can position with the display framing. One hole per revolution results in an absolute position encoder.
Spinning Mirror Display
A somewhat simpler mechanical variation on the Nipkow drum is to spin a planar mirror from which is reflected light from a vertical column of LEDs. Each LED modulates a line of the display. The curvature problem of the Nipkow drum still exists but can be similarly corrected. The LED pixel light source is to the left, along the –x axis, shining to the right, and its beam impinges on the mirror at the location of its spin axis. The angle of incidence of the beam with respect to the plane of the mirror equals the reflectance angle. If the mirror angle, θ = 45°, then the reflected beam is upward and projects upon the screen x -axis at its midscreen origin. For the more general case, as shown below, the beam location on the screen is a function of θ .
Then applying basic trigonometry,
Over a range of 0 to 90o , the mirror sweeps out the full range of x (+/- ∞ ). If the swept range is limited to +/-30o (+/- π /6) around 45o ( π /4), or 15o to 75o ( π /12, 5 x π /12), then the x -axis screen width is +/-R x tan( π /6) = . Curvature correction for the spinning mirror occurs in time, as for the Nipkow drum. If the mirror is spun on a horizontal axis instead, then curvature correction can be performed on voltage instead of time – an easier task – though 25 % more LEDs will be required for a ‘scope screen aspect ratio with square pixels. Consequently, x is changed to y and the spin axis rotated 90o . Now, ordinary pincushion correction can be applied to the vertical waveform (using translinear circuits) to produce
If the incident LED beam is located off the spin axis of the mirror by a position error of ε , the point of reflection is no longer stationary but translates to the left during the screen scan by an amount ε x cos θ . It is nulled out by a positioning adjustment. If the linear axis of LEDs, as an array, is warped so that some of the LEDs are not on-axis, then position error up to ε in extent will occur as image distortion on the screen. This error can be compensated electronically, though not without even more (analog or μC) computation. Nipkow drum wobble will cause a similar kind of distortion and both are limiting factors in the performance of these kinds of electromechanical displays.
A scheme that is conceptually closest to a CRT is a vertical LED column with a step-motor translational sweep. The horizontal sweeper moves the LED array driven by a time-base that drives the position controller of the motor. If the LEDs are behind a long-persistence phosphor sheet, then the motor dynamic requirements might be reduced. Without it, what is the best repetition rate that step-motors can be expected to achieve?
The load of an LED array and hence the rotational inertia is insignificant. If the step-motor were to drive a rack and pinion gear, a mechanical acceleration can be achieved of Δ 40 Hz me/15 ms = 2.67 kHz me/s with a size 34 step-motor. Then for a pinion radius of 1 cm/2 x π ≈ 0.159 cm, its circumference is 1 cm, one revolution (rev) will result in a linear change of 1 cm, and the maximum linear acceleration is a = 26.7 m/s2 . Let the screen width again be W = 5 cm.
The motor would require maximum acceleration to the left of the screen, then constant speed, U , across the screen and maximum deceleration off the right side. This trapezoidal speed function must repeat twice per sweep: the sweep itself and the retrace, which need not be blanked as in a ‘scope. If the acceleration and deceleration times are the same, together they are
and the constant-speed sweep interval is
Then the sweep period is
For U to be a real number, the maximum f occurs when
Also, ta ≈ 75 ms and ts ≈ 61.2 ms. The off-screen distance exceeds the screen width, as is typical in an analog ‘scope at the higher sweep rates.
The maximum f barely meets the required screen refresh rate of 30 Hz, for which f = 60 Hz. However, for a ‘scope-like display, this might be a (barely) acceptable solution. A motor drive is required which is power electronics instead of instrumentation.
Besides the above schemes, other electromechanical scanners could be based on wobbling or spinning mirrors in two dimensions, as in bar-code scanners. Past novelties have been demonstrated, such as a line of LEDs mounted on a hacksaw blade that sways back and forth like an inverted pendulum, kept going by a solenoid. This scheme has some of the major properties of the Nipkow disk except that the LEDs are moving, yet can be connected at the stationary end of the blade without sliding electrical contacts. Audio speakers also present possibilities in that a 2D vibration set up on a mirrored cone performs an area (2D) sweep, though in a Lissajous and not a raster pattern. A speaker is a linear motor with a limited stroke length. If extended, it could pull a line of LEDs back and forth.
The advantage of electromechanical displays is that viewers without engineering knowledge can see in general how they work. Partly because of this, they attract attention and are a marvel to behold in themselves. This two-part article ventured into some of the technical complications that reveal why LCD and LED or even CRT all-electronic displays are far more practical. Even so, creative minds look for and are stimulated by ideas that might not be refined enough to compete with existing solutions to problems. Micro-electromechanical technology, such as the TI “mirror array on a chip” could change that, though the mechanics are small and distributed rather than singular and macro-sized. The Maker Fair 3D spherical display, however, shows that inventors are still exploring the possibilities of electromechanical displays.