Part 1: Desk Concept Updates
Over the past week, I first made updates to my design spreadsheet. Firstly, I increased my total allowable error to 5mm in my error apportionment. Previously this was set to 2.5mm which I realised might have been too tight for a desk. With this larger allowable error, I re-optimized the sizes of a few members, namely the base members and the rail. I managed to switch back to wood for all the members to achieve the desired overall stiffness. I also switched the type of wood to solid softwood from plywood.
Summary of dimensional changes:
Width and thickness of rail (member 2) now 4"x4"
Width and height of member 3 now 4"x4"
Width and height of member 4 now 4"x2"
The second big update to the spreadsheet, was the calculation of the reaction forces at the base of the table to ensure that the table does not tip forward or sideways, given a 300N point load at the tip of the table or on far edge of the table respectively. For wooden members, the spreadsheet estimated that the lengths of base members be 0.7m for member 3 and 0.5m for member 4. For these values, the reaction forces have the right sign which indicates that the members are still in contact with the ground.
The updated spreadsheet can be downloaded below.
Link to updated Spreadsheet
Part 2: Error Budget
With the first order analysis of my desk showing promise for a feasible design, I was ready to move into performing the error budget for the chosen concept. Professor Slocum's "Monster" Error Budget Spreadsheet was used for this detailed error analysis.
For my design, I would require 4 coordinate axes to map errors: 1 at the slider, 2 at the base of the vertical rail, 3' and 3" at the ends of base member 3 and finally 4' and 4" at the end of member 4.
The coordinate systems and loads were appropriately entered into the CS and Loads Tab of the spreadsheet. For the loads at the centres of stiffnesses of the Coordinate Centres, I was unsure whether I would need to include the moments and loads due to the weight of the members. The confusion arose because the Error Budget for Bridge Machine, did not factor in the weights of the members in the CSs and Loads Tab of the spreadsheet.
The compliance matrices were derived as shown below.
After deriving the necessary matrices, I entered them into the appropriate locations in the Error Budget Spreadsheet. I also entered points of attachment of one coordinate system wrt the point of interest of the next system. I was unsure of the stiffness of a bolted joint so I entered a rough estimate.
My spreadsheet can be downloaded from the link below.