Chief Delphi



The ScooshA novel solution for linear motionGus “GeeTwo” Michel II, mentor for FIRST Robotics Competition Team 3946Scoosh (n.) a curved device which converts rotational motion into horizontal motion, fm. scoot + swooshProblem: The 2017 FIRST Robotics Competition game, FIRST STEAMworks, included a task of placing an 11 inch diameter plastic gear on a 10.5” long spring “peg” to be lifted by a pilot (human player) into the airship to be used to start its rotors. The gear has plenty of open space in the inner 6.7” diameter circle. Our original concept was to hold the gear in a vertical orientation just inside the robot’s frame perimeter, and drive into the peg so the pilot could lift the gear out of the gear pocket. Early in the build season, there were concerns (later justified) that the pegs would droop and gears would fall off the peg, particularly if the gear were hung near the end of the peg away from the lift end. As we did not want to carry the gear outside of the frame perimeter, we determined that we needed some mechanism to push the gear out several inches, at least beyond the ends of the bumper. Strategic considerations also required that this mechanism be as lightweight as possible, while having the necessary resilience and reliability required of a mechanism that reaches outside of the frame perimeter.Early Solutions: Rack-and-pinion, an arm which rotates about a horizontal axis and lead screw solutions were all considered. Rack and pinion was determined to be beyond our manufacturing capability. A straight arm would not push the gear evenly, but tend to push it down at the end of the stroke, which was not desired. We built a lead screw prototype, but the weight and volume were more than we wanted to commit to this mechanism. One of the students suggested that if the arm in the second case were curved backwards, it could push the gear forwards without pushing it down. This concept later resurfaced, and a few minutes of playing with a twist tie hinted that a solution to the problem existed. This solution became the scoosh.Problem restatement: Design and build a mechanism with a single degree of freedom - it rotates about a fixed horizontal axis. As this mechanism rotates, it must present a vertical face at a constant altitude which is several inches above the axis of rotation and which moves horizontally.Mathematical Formulation: A couple of hours on Google and Wolfram Alpha did not yield any solutions to this problem, so it was time to draw a picture, define some variables, and hit the integral tables. The desired shape is approximated here with part of an ellipse.Figure SEQ Figure \* ARABIC 1: Derivation of the equation of the scoosh shapeFor convenience, the offset “h” was set to unity. The condition that the shape is vertical at height h is given by rdθdr=tan?= r2-1, or more simply dθdr=r2-1r. The solution to this equation is: θ=r2-1-sec-1r. Clearly, any solution at r<1 would not result in pushing the gear; this part of the shape is required in order to transmit the torque from the axis of rotation to the functional portion of the shapeCuriously, the intersection of the scoosh with the offset line is a linear function of the rotation angle of the scoosh. That is, for angles measured in radians, d = ? + θ. This is a result of the “lever arm” for the conversion of torque to force being a constant value, h. For large values of r, the shape approximates a simple spiral which r increases by 2πh per revolution.Practical Considerations: Due to the mechanical requirement for a hub to transfer torque from the driving motor to the scoosh, it is impractical to have the axis of rotation in the plane of applied force. This is resolved by “pre-rotating” the shape by a small angle and restoring the torque transference to a vertical plane. The shape must also continue below the axis by a small amount to support the hub. The other remaining design parameter is the desired length of travel. The spreadsheet accompanying this paper will calculate and draw the shape of the scoosh face from these four design variables. Note that it is not necessary that b=d0, nor that the rotational range be approximately 90 degrees. Because the travel is proportional to the offset times the angle of rotation, the rotational range will be Δd/h radians.Figure SEQ Figure \* ARABIC 2: Input variables for design spreadsheetNote also that the center of the red circle is the axis of rotation.In addition to drawing the shape in its charts, the spreadsheet also numerically calculates the length of the curve and overall height and depth of the shape to support fabrication in columns J, H, and I and copies these length to cells C7 through C9. Because everything is scaled to the offset h, all of the numbers in the spreadsheet are dimensionless. The output graphics provided with the posted spreadsheet are presented in inches. To use this spreadsheet for metric fabrication, it would be easier to reconfigure the axes of the drawings and use metric units in the spreadsheet.Fabrication: While a scoosh can obviously be fabricated in many different ways, I will outline the steps used by team 3946 to show how such a shape may be fabricated using fairly basic tools: a letter-size printer, rotary saw, utility knife, jig saw, belt sander, heat gun, and handheld drill.228600039624000The required geometry was determined and printed. The initial values in the spreadsheet are the actual values used by 3946 for competition in 2017. A sheet of polycarbonate was cut using a jigsaw using a plastic-cutting blade at low speed to the shape pictured at right. The height was determined from the “total curve length” in the spreadsheet, and the width was determined by robot geometry and the size of the gear. This shape has three “tines” so that the 1” diameter peg could pass through the shape, but fuel (5” diameter balls) could not.2286000683895Figure SEQ Figure \* ARABIC 3: Scoosh cut planFigure SEQ Figure \* ARABIC 3: Scoosh cut planA 2x8 board was ripped down to 6-1/4”, though this step could be skipped if you do not have access to a table saw.The printed copy of the curve was folded at right angles at the leading face and lower edge, placed over the corner of the board, and the curve was transferred to the board using a utility knife. The board was then cut along this curve using a jig saw, and smoothed with a belt sander.Steps 4 & 5 were repeated to make two more lumber shapes, so we would have one for each tine of the final scoosh. One of these was 1-1/2” shorter at the square end to facilitate construction of the template.235585-32385004591054312920Figure SEQ Figure \* ARABIC 4: Scoosh templatesFigure 4: Scoosh templatesThese shaped pieces of lumber were assembled using wood glue and clamps, along with some ?” quarter round and ?” plywood into a form to serve as a template for the polycarbonate scoosh. Figure 4, at left, shows an earlier iteration of the scoosh template in the foreground and the nearly-completed competition scoosh template in the background.The polycarbonate tines and flaps were then heated with the hot air gun and curved to conform with the wooden template. (Heavy gloves or oven mitts recommended!)106680169608500 Holes were drilled 1” behind the leading face and 1” above the base to support the hubs, and for the machine screws which secure the hubs to the polycarbonate. Our scoosh uses two different hubs because one side is driven by the 6mm D shaft which is part of the motor and the other is driven by a ?” round shaft which extends the motor shaft.32632653989705Figure SEQ Figure \* ARABIC 5: Scoosh installed in Ludwig, 3946's practice robot (Near side baffle has been removed for visibility)0Figure 5: Scoosh installed in Ludwig, 3946's practice robot (Near side baffle has been removed for visibility)The hubs were installed and placed on a shaft driven by a NeveRest 60 motor. A servo was also considered for this function, but we determined that we could meet the force and speed requirements more readily with the gear motor and encoder than with a servo. As can be seen in the photograph, we held the gear in place against the vertical scoosh with doors mounted on springs. When the scoosh was actuated it pushed the gear against the doors, opening them. Fortuitously, when the doors were open sufficiently to allow the gear through, the scoosh was under some tension, and the release of the door force pushed the gear gently along the peg several inches past the design petition results: Due to problems with integration of the robot software, the scoosh has not been properly tested in a competition scenario. Based on in-shop and demonstration performance, there is some difficulty hanging a gear if the robot is too close to the base of the spring, because the doors do not open sufficiently to allow the gear to exit the robot. This will be resolved in further iteration of the scoosh. ................
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