After coming to a rough finalization of our crank arm design, basic calculations of the crank’s kinematic diagram showed that in order to open the bag, the force exerted on the bag by the L7L6 linkage needed to be twice of that required to pull the bag under normal conditions. In order to help increase the force of the L7L6 linkage, a rubber strip was applied to the inside of the wooden box’s hook mechanism in order to increase the friction between the hook and the bag, allowing for the crank to apply more force thanks to the associated friction helping pull one side of the bag in the opposite direction of the crank. After these hand calculations, we shifted our views to a virtual MATLAB simulation, where we performed the motion analysis for several significant parameters in the mechanism, mostly in regards to θ2, the angle of the motor gear. A complete document containing all of the MATLAB code can be found within the Appendix section of this project page.
Figure #3.2: Diagrams showcasing a counter-clockwise rotation of the machine, demonstrating how the mechanism pulls the slider bar backwards, in addition to defining many of the significant parameters used during the MATLAB analysis
Figure #3.3: Complete compilation of all MATLAB motion analysis graphs, featuring θ3, θp, d, b, ω3, ddot, and bdot as a function of θ2, in addition to the position of point P (the end of the claw) in relation to O2
Due to the nature of our machine having two degrees of freedom rather than simply just having one, the mechanism's full range linkage operation could not be rendered in a tool such as Planar Mechanism Kinematic Simulator. Instead, the linkage operation was animated within SolidWorks, as seen in the annotated video below:
Figure #3.4: Annotated animation of the full assembly as seen within SolidWorks
As seen in the video provided in Figure #3.4, the mechanism travels between four different parts over the course of one single cycle. Part A being the beginning of the counter-clockwise rotation with the motor pin starting at a 0° angle until the slider above the motor gear reaches its leftmost position in order to have the "claw" part of the arm clamp down on the bag. From here, Part B begins, consisting of the slider arm pulling backwards until the motor pin reaches an 180° angle. Part C and Part D are close to being inverses of Part A and Part B respectively, with Part C involving the motor gear slider moving back to its rightmost position in order to release the "claw" part of the arm from its clamping position and Part D moving the slider arm back forward. After Part D, Part A begins once again, repeating the entire process. These four parts are annotated within all eight graphs in Figure #3.3.
Analysis - In Detail
The following details our motion analysis of the system.
The system's motion is divided up into 4 parts.
Thus, for Parts A and C, length b changes, and length d is constant. For Parts B and D, the mechanism is a simple slider crank with length b constant and length d changing. Thus, Parts B and D can be analyzed using the slider crank motion equations while Parts A and C can be solved using vector loop analysis.
Boundary Conditions
The boundary conditions governing the transitions between Parts A and B and between Parts C and D are based on the geometry of the mechanism when the internal slider bottoms out. For this, the Law of Cosines can be used.
For the boundary between Parts A and B:
For the boundary between Parts C and D:
Vector Loop Analysis
Parts A and C
For Parts A and C, the vector loop analyses are the same, but the lengths are different. So, to more easily solve them, a generic system can be solved once and the dimensions for Parts A and C applied to it.
Position Analysis
Velocity Analysis
Result
For Part A:
For Part C:
Parts B and D
For Parts B and D, the equations for a simple slider crank can be used.