Kinematic Analysis and Synthesis (Group 15, 2023)

A complete document containing all of the MATLAB code and the SolidWorks assembly can be found within the Appendix 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, θ_p, d, b, ω₃, d_dot, and b_dot 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 using the Motion Analysis add-on, 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. More in depth motion analysis calculations can be seen below.

Analysis - In Detail

The following section details our motion analysis of the system. The dimensions used in this analysis is shown below in Figure #3.5

Figure #3.5: Diagram showing the basic dimensions of the mechanism

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:

Figure #3.6: Diagram showing the basic dimensions of the mechanism at the boundary between Parts A and B

For the boundary between Parts C and D:

Figure #3.7: Diagram showing the basic dimensions of the mechanism at 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.

Figure #3.8: Diagram showing the vector loop used for analyzing Parts A and C

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.

Result