Equatorial Telescope Platform

This article describes a new equatorial table design for Dobsonian telescopes. It is easy to ... Page 1 of 3

Equatorial Telescope Platform This article describes a new equatorial table design for Dobsonian telescopes. It is easy to construct with woodworking tools and hardware store parts. The mount uses casters, flat pieces of aluminum and teflon pads for bearing surfaces. The mount was designed because I needed a table for my 17.5" Dobsonian, but the center of mass of my system seemed too high for the standard equatorial platform designs I had seen, and required rather complex (by my standards!) curved bearing surfaces. I decided to see if a table that used only plane surfaces could be designed that could be made from "hardware store" parts, and could be made so that the system was neutrally stable (wouldn't tip over or rotate back to vertical if not held - ie rotates about the center of mass). To my surprise, a design was found that met all of my requirements. The heart of the system is 4 non-swiveling casters running on 4 pieces on aluminum "angle iron". By proper choice of the spacing and angles of these four planes, the mount moves in such a way as to rotate around an axis parallel to the earth's axis. How it Works

The operation of the mount is not at all obvious! The principle behind the bearings and the motion of the mount is shown in fig.1 fig.1.. The stance is the horizontal distance between the centers of the casters when the table is horizontal. If a platform is constructed so as to have two points in contact with the outside of  an isosceles triangle, the point on the platform corresponding to the apex of the triangle, when the platform is horizontal as shown, will translate exactly horizontally! Note that as long as the point that translates horizontally is the center of mass, the system is neutrally stable. The fact that this point continues to move horizontally as the points of contact move up and down the sides of the triangle is not at all obvious at first glance, and was determined empirically at first from fairly elaborate computer calculations which calculated the motion of various points on the platform. Once it was apparent what was occurring, an analytic proof was developed. If one were on the equator, pieces of two identical triangles, one on the north end of the platform and one on the south, would be all that is needed. However, for other latitudes, the two triangles have to be of different heights (the tall one on the end nearest the pole), and the triangles have to be tipped toward the equator. Figure 2 shows a side view of the system, looking to the west. The line between the apexes of the two triangles goes through the center of mass of the combination of the telescope and moving part of the equatorial table. There is one additional constraint that could have defeated this scheme. The platform ties together the north and south bearings. If the horizontal translation for 1 degree of rotation for the two bearings is not equal, the platform will try to twist and the rotation axis will try to swing horizontally. Fortunately there is a degree of freedom on the design that can be used to make sure that this constraint is met. Once the north-south separation of the two triangles is fixed (for example by the size of the base of the telescope mount), the heights of the two triangles are not adjustable since the line between the apexes of the triangles should go through the center-of-mass of the telescope. However, the "stance", (the distance in an east-west direction between the caster centers), of the two triangles is adjustable. This degree of  freedom provides a solution where the translation of the north and south ends matches. Figure 3(a) displays the north triangle angle and stance for my telescope. I decided that angles up to 60 degrees on the north triangle could be tolerated (the south triangle is shallower). That results in a south stance of 95 cm, a north stance of 82 cm and a south angle of 41 degrees. Other configurations with centers of mass lower have solutions that involve shallower angles. Figure 3(b) shows the relationship between N-S distance and the height of the center-of-mass above the base of the triangle (the line through the caster

This article describes a new equatorial table design for Dobsonian telescopes. It is easy to ... Page 2 of 3

centers). For this example the angles of the north and south triangles are fixed at 60 and 45 degrees, respectively. Both fig.3(a) and (b) are for a latitude of 34 degrees. The appendix gives the analytic formulas to calculate the angles of the plane surfaces. Construction of the Mount

Since I had an uneasy feeling about some hidden "gotcha" in the design, I built a working test version of  the mount out of 3/4 inch particle board, 2 X 4s, 1.5 inch wide extruded aluminum "angle iron" (Lshaped cross section) attached to pieces of wood to hold them at the correct angle, and casters with 2 inch diameter plastic wheels to run along these surfaces. Since these surfaces are tipped to the south, the casters would roll off the tracks if not prevented. To counter this thrust, there is a teflon pad riding on the other leg of the "L" on the south triangle. This also removes the side load from the casters. A caster was not used in place of the teflon because the point of contact describes a shallow arc instead of a straight line. The test mount worked as designed, so I constructed a more compact (and aesthetically pleasing!) mount for use with my telescope. The major change in the second mount was in the way that the aluminum tracks are held at their correct angles. I cast the tracks into the edge of a pyramid made out of "Quik-Fix All-Purpose Patching Compound". A form was made out of Masonite with the correct angles, and the aluminum piece was laid inside the form before it was poured. Small pieces of aluminum "angle iron" were epoxied onto the underside of the track to make sure that it wouldn't come off of the casting. The form was made symmetrically, so that one form could be used for both sides of the triangle; a different form was made for the other triangle. The lengths of the tracks was chosen to give about 40 minutes of  operation. The mount is kinematically over-constrained (its like a table with 4 legs instead of three). This does not appear to be a major problem, however. If the tracks that the casters roll on are made adjustable in position or angle, errors in construction can be corrected after the mount is built. Also, with the order of  100 pounds on the mount, flexing in the structure tends to distribute the load onto all four casters. Similar arguments apply to the two teflon pads holding it laterally (only one is needed from a kinematic standpoint). Figure 4 shows the two halves of the mount. Figure 5 shows the two halves together with the mount looking all the way to the east. Both fig. 4 and 5 were taken before the jack-screw was installed. The mount was "motorized" by running a jack screw between the upper and lower halves. Both ends of  the jack screw are pivoted since the angle between the screw and the two surfaces changes as the mount tips. A geared-down DC motor was used to turn the screw through a belt/pulley arrangement. The motor is driven by a variable-voltage DC supply which is controlled from a small hand-held box which has controls for forward/reverse and guide/slew. The guide speed is continuously adjustable through a potentiometer in the box. The box also has a red LED mounted on the end to act as a flashlight. Figure 6 is a close-up of the original jack screw and controller; I have recently replaced the DC motor in the original configuration with a stepper motor controlled by the parallel port of a computer, which allows me to compensate for the variable tracking rate automatically. Figure 7 shows the mount with my 17.5" telescope mounted on it. The controller is stored on the side with Velcro. Note the hinged block of wood between the upper and lower halves of the mount, this prevents excessive stress being put on the jack screw when the mount is rolled out of my garage on to the sidewalk; there is a similar one on the east side. The wooden tray on the rear of the telescope takes Scuba diving weights as counterbalances. The power supply and the driver for the stepper motor fits into the space between the upper and lower halves of the mount. I have been pleased with the performance of the mount for visual observing and for use with my

This article describes a new equatorial table design for Dobsonian telescopes. It is easy to ... Page 3 of 3

spectrometer. I have the platform mounted on 4 casters and I can roll my whole telescope assembly out of my garage onto the sidewalk and line up the edge of the mount with the edge of the sidewalk (the street runs N-S). The computer that drives the stepper motor moves the mount to its most easternpointing position (runs it in reverse at high speed until a microswitch closes), then steps at a variable rate as it tracks to the west. The computer also monitors switches on a hand-controller to increase or decrease the stepping rate momentarily to correct for any tracking errors. My spectrometer has a slit that is only 2.5 arcseconds on the sky, and if the wind isn't blowing too hard, I can keep the star on the slit a fair fraction of the time. The program Eqmpiers.bas calculates the size and location of the pyramidal piers that contain the tracks for the mount. Once that calculation has been done, the program Pierside.bas will calculate the sides of  the pyramid. The geometry is shown in fig. 8 . APPENDIX

Definitions: a : angle of the triangle (90 degrees is vertical) h : height of triangle (base to vertex) s : stance (base of triangle, caster center-to- center) y : north - south distance between triangles xcm : east - west position on the center-of-mass zcm : vertical distance of the center-of-mass from base of triangle (not height of triangle) t : theta, the rotation angle around the polar axis e : epsilon, the latitude of the observing site An appended subscript "s" or "n" to the above definitions refers to the north or south triangles. The relationship between the north-south distance between triangles, the latitude and the height of the center-of-mass is: hs = zcm - y*tangent(e)/2 hn = zcm + y*tangent(e)/2 The constraint that the translation be the same at the two ends of the polar axis amounts to setting the derivative, d(xcm) /d(t) = h*cos(t)/ sin 2(a) = h / sin2(a) equal for the north and south ends at theta = 0. The equation for the stance of the north triangle in terms of the other variables is sn2 = ss2*hn /hs + 4*hn*(hs - hn).