Kinematic Analysis and Prototyping II - Team 9
The information in this section will build upon the information presented in the previous Kinematic Analysis and Prototyping section. The goal of the mechanism remains the same, though the analysis and ideal profile of the mechanism have changed as a result of reducing scope. Because the two iterations -this prototype and the one displayed in the previous section- were so different, a second page has been created to further describe the development behind the iteration that became the final prototype.
Ideal Profiles
From the construction of the previous iteration, we realized that if we plan on using a linearly actuated end effector, the ideal profile of the mechanism must include a linear portion of travel to isolate the actuation of the end effector relative to the curvilinear rotational component of moving the package from one surface to another. In short, the end effector must be allowed to open and close fully before the entire system begins to rotate. A diagram of this proposed ideal pathway is outlined below. The blue sections indicate the linear travel, in which the end effector is being actuated by the linkage system. The black sections indicate the rotational movement of the package and the overall linkage system.
The previous iteration ran into several issues with binding- points at which the mechanism interferes with itself and can no longer rotate due to friction/sharp corners. This shifted us onto the path of considering multiple four-bar linkages coupled to each other to output a complex motion profile.
Construction of a Model
We began by considering the concept of a simple partial scissor lift to accomplish the linear motion of the mechanism. Scissor lifts have some very convenient properties for our uses. If you ground a single joint and expand/contract the mechanism while rotating the entire scissor lift about that ground point, the joint opposite to the grounded expands and contracts colinearly with the grounded joint. For purposes of this project, this ungrounded opposite joint is considered the output joint. This is the first four-bar mechanism. The parameters that drive this design were determined by package and location constraints (i.e. size and shape of the package, distance between pickup and dropoff locations, degree of rotation).
Now, if another scissor lift is coupled to that already existing scissor lift, the original two points (grounded and opposite to grounded joint) AND an additional point in between the two from the newly coupled scissor lift remain colinear to each other over the entire operation of the mechanism. The newly coupled scissor lift is the second four-bar mechanism. The lengths of these links were determined based on desired overall expansion and contraction limits with the help of some geometry.
Finally, the mechanism now just needs to follow the ideal rotational and linear paths outined in the Ideal Profiles section above. Since all three of the joints mentioned above move colinearly, it is possible to choose to attach the final four-bar mechanism to either the middle joint or the output joint. To produce the most linear travel, the middle point was chosen as the attachment point. The goal of the mechanism is to rotate 90 degrees from a single rotational actuator, thus, the coupled four-bar mechanism needs to achieve a quarter-circle output path given a full circle rotational input. This is the final four-bar mechanism. The link lengths are determined through geometry. At minimum and maximum output link position, the input link and the coupling link become colinear, creating a triangle that can be used to determine lengths through the Law of Cosines.
Taking advantage of all of these properties of various four-bars, a final constructed model that follows the ideal paths almostly perfectly may be produced. The motion profile of this mechanism will be compared in depth with ideal pathways in the next section, Positional Analysis.
Positional Analysis
The following graphs display the projected pathway of the output joint. All of the following positional analysis was conducted through MotionGen.
The most important aspect to highlight is the difference in projected motion profile compared to the previous iteration shown below.
The above model is an approximation without the presence of the slot that caused binding, simulating a close to realistic manufacturable model. The first iteration's motion profile was extremely curvilinear, with almost no linear or close to linear portion to allow the linearly actuated end effector to close before the entire system started rotating. This, along with many other factors, made the first iteration completely unrealistic for the final model. In comparison, the second and final iteration's motion profile achieves very close to linear if not linear portions at the ends of its travel, allowing for isolation of the end effector motion. The redesigned linkage system also eliminates the need for slots and the potential for binding of the system due to sharp corners and friction as the entire system is driven by revolute joints.
Another useful quirk of the final redesigned mechanism is the tuneable displacements for the pick up and drop off phases. This is done by adjusting the length of the coupling link in the final four bar mechanism driving the rotation of the system. It can be seen from the positional analysis of the second iteration that the displacement for the pick up phase is larger than the drop off phase- this is done on purpose to demonstrate that the mechanism allows for partial actuation of the end effector. This becomes useful in situations where the end effector must constrain its fully open position, for example, in tight drop off or pickup zones where packages are placed closely together.
End Effector Speculation
By design, the three points on the partial scissor lifts remain colinear throughout the entire operation of the mechanism. This lends itself to the design of a linearly actuated end effector. We considered multiple methods of actuation, the main two being link/slot actuated and rack and pinion actuated. The two iterations of link/slot actuation are highlighted in the previous Kinematic Analysis and Prototyping section. In this section, the rack and pinion iteration will be described in further detail. Below is a proposed model of a rack and pinion system with a dwell period, to account for when the mechanism is rotating and there is undesired expansion of the coupled partial scissor lift system that actuates the end effector.
The toothed part of the rack drives the actuation of the end effector as the pinion gear is allowed to rotate when meshed with the rack. This is the actuation phase, where any movement of the linkage system will result in actuation of the end effector. This is planned to be coupled to the linear portion of the linkage system pathway, allowing for isolation of end effector motion. The untoothed part of the rack then converts the rotational motion of the pinin gear to a linear motion as the teeth slide along the smooth rack. This is the dwell phase, where any movement of the linkage system will not result in actuation of the end effector. This is ideally coupled to the rotational quarter circle motion of the linkage system motion profile, where constant contact on the package must be maintained and consequently when the end effector must maintain its position. This end effector will be pinned to the output joint and slotted to the middle joint, taking advantage of the colinear movement as a linear input.
Previous Page: Kinematic Analysis and Prototyping I
Next Page: Manufacturing and Prototype Iterations
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