Prototyping

 The goal of the project was to design a trashcan with a tray mechanism that allows users to place trash on the tray and the tray rotates (without spilling the trash) to deliver the trash sideways into a hole in the trashcan.

Multiple attempts were made to use perpendicular bisects at the pivot points and figure out the solution to the complicated mechanism motion of the trays path (including offsetting the pivot vertically from the tray, hence the triangles). In the end, there is a simple formula to calculate the position and length of each member. When fully extended to the left corner, the short link plus the distance between the pivots of the two links must be equal to the long link plus the distance between the attachments to the tray. Below is a numerical explanation of this.

Mathematical Relations

 In order to perfectly cross the trays motion over the corner of the trashcan, the tray must reach a perfect 45 degree angle off the corner (indicated by the dotted line). Along this line, the equation A + B = C + D must be true to achieve the right alignment across this point in it's motion, otherwise one of the links will flip the tray. The distances A, B, C, and D are labeled in the drawing to the right.

Finally, the links are placed on opposite sides of the trashcan so that free motion can be achieved within the mechanism using the least amount of material and fasteners.