Kinematic Analysis and Prototyping I - Team 9

Problem Statement

This section will focus on the design and construction of the manipulator, which should lower, open, and grab an object, then rotate and place the object on a drop-off surface 90 degrees relative to the pick-up surface. Ideally, the end effector should be perfectly synchronized with the rotating linkage system, opening as the linkage system expands and closing as the linkage system contracts. For reference purposes, a diagram of the linkage system, end effector system, and its various components are provided below.

Linkage System First Iteration End Effector Second Iteration End Effector Concept

Red- lower scissor lift links Orange- end effector links Dark blue- end effector links

Blue- upper scissor lift links Tan - T slot Green- L bracket

Pink- input link Red- lower scissor lift links Light pink- secondary links

Green- path slot Dark purple- manipulator path slot Dark purple- input link

Critical points (1, 2) are numbered in orange Light purple- input bracket

Ideal Profiles

An ideal mechanism path would achieve perfect linear motion of the output point as the linkage system reaches 90 degrees and 0 degrees relative to the ground, allowing for the isolation of the grabber mechanism movement relative to the rotational component of the overall system. This ideal linkage system input path is demonstrated in the curved slot and full linkage system below.

Ideal Linkage System Input Link Path Animations

The force profile/mechanical advantage of the end effector should ideally peak at the maximum close position to maintain adequate contact with the object being picked up. The plot below demonstrates a possible ideal plot of mechanical advantage, with a peak mechanical advantage at small linear displacements (indicating a closed configuration for iteration one). For future iterations, a better alternative would be to design a system that achieves a mechanical advantage that approaches infinity as the linear displacement decreases.

Ideal Mechanical Advantage Plot for Iteration One Type End Effectors

Mobility Analysis

Mobility Calculations for Linkage-End Effector System

Positional Analysis

We chose to focus on the kinematic/position analysis for the overall linkage system because its motion determines the opening/closing/position of the end effector and the rotation/displacement of the package volume.

Through prototyping, it was found that the ideal motion path was not possible using a sharp-cornered curved slot. Thus, kinematic analysis was performed on a similar system using a constant radius slotted input link to simulate the effect of the linear component of the ideal path. The position analysis and generated positional graphs of the output point below are obtained through MotionGen.

Position Analysis of Output Point

Associated Displacement, Velocity, and Acceleration Graphs

The results of the kinematic analysis demonstrate that using a constant radius input link without a linear component to the path results in poor synchronization between the end effector and the rotating linkage system. It can be easily seen from the animation that the relative distance between the critical points changes throughout the entire rotation path, indicating that the end effector will open and close while the linkage system is not in its optimal 90 degree and 0 degree position (pick up and drop off position). Moving forward, we would like to explore the effects of a multi-radius slot path that is both manufacturable and isolates change in distance between critical points to optimal points in the rotation.

Mechanical Advantage Analysis

The analysis below will focus on the end effector. We chose to focus on the mechanical advantage of the end effector because the main goal of the end effector is to maintain adequate package contact through force applied from the end effector links.

First Iteration Animation Second Iteration Animation

First Iteration Mechanical Advantage Plot Second Iteration Mechanical Advantage

From the graphs above, it can be seen that the second iteration has a slightly more favorable mechanical advantage trend than the first iteration does. With the first iteration, the mechanical advantage peaks when the mechanism opens and drops when the mechanism closes. This is validated by the fact that the mechanism moves quickly when approaching the vertical portion of the curved slot as the vertical input force aligns with the direction of motion. The second iteration continues to have the same issue, where mechanical advantage peaks at an open configuration. It's worth noting that the reason for iteration was purely as a proof of concept for a redesign due to manufacturing concerns with slots overconstraining the system and providing excess friction.

For future iterations, the movement of the joints constraining end effector link motion needs to be inverted, initially moving with a vertical downward portion of the arc and ending with the horizontal portion of the arc for opening and vice versa for closing. To further increase the mechanical advantage, we would like to pursue lever stacking, in which multiple levers are coupled together to vastly increase the force output. As the second iteration proved, slots overconstrain the design of our system, which means that our project will likely not include slotted pathways in the final iteration.

Physical Prototype Design Process

Identify constraints
1. Set boundaries on what type of object is being moved (shape, size) and where it's being moved
2. Clarify assumptions- we are moving the object onto a conveyor belt, which moves the object outside of the grasp of the mechanism without the mechanism needing to retract its position as it's placing
Construct ideal input pathways
Establish general trends (kinematic, force)
1. Created parameterized code that generated force and motion profiles
Design prototype using general trends and ideal input pathways
Construct prototype
Conduct in-depth analysis for areas of interest
Iterate on prototype design using analysis results

Future Timeline

Weekend of 11/10-11/13: Design iteration, final design changes, final analyses conducted

Week of 11/13-11/17: Begin physical iteration of prototype

Week of 11/20-11/24: Finalize iterations of the prototype, begin constructing the final product

Week of 11/27-11/29: Final product construction complete

11/29: Demo Day

Physical Prototype of First Iteration End Effector

In-Progress Physical Prototype of Second Iteration End Effector

Prototyping Reflection

The most important thing we learned from prototyping is that not everything that works in Solidworks will work in real life. The sharp corner in the input link path slot that was projected to work in Solidworks caused the system to bind in the physical prototype. Furthermore, material choice is important, especially in planar systems that require a low coefficient of friction for links to slide against each other or against slots. When we originally used wood, the friction between the slot and the dowel massively increased the input force required to move the mechanism, greatly decreasing the mechanical advantage of the system. When talking to the TAs, we learned that we can create PETG inserts (PETG has one of the lowest coefficients of friction out of all the materials in TIW) that interface between the slots and the dowels to prevent the system from binding due to friction. We have since learned from the first iteration as the second iteration of the end effector was made out of acrylic, which made a noticeable difference in terms of smooth mechanism movement. Furthermore, for the first iteration of the end effector specifically, prototyping made our group realize that the slots in the end effector assembly were redundant and over-constraining the system/adding unnecessary friction.

In terms of workflow, prototyping emphasized the importance of good analysis before jumping into design. Since all three of us are more versed in modeling than in mathematical simulation, we were tempted to jump straight into physical design without doing the proper mathematical analysis. This caused us to waste a lot of time and energy adjusting parameters to create effects we were not familiar with and also to end up with a product that performed badly in terms of kinematic and mechanical advantage. This is the reason why both iterations of the end effector generated low mechanical advantage values at the critical closed position. We have since asked for help with the mathematical side of the analysis and we now have a good understanding of where to go from here.

Future Tasks

Having received some feedback from both the TAs and our own analyses we conducted, we recognize that we have a long way to go in terms of design iteration. Since we now have a better understanding of how to approach the end effector especially, those force graphs need to be optimized using the methods mentioned in the mechanical advantage analysis section (i.e. stacking levers, shifting the slot path position). The linkage system also needs a redesign of the slotted paths, incorporating a variable radii curve instead of sharp transitions from curved paths to linear paths. Design is projected to be done by the end of this weekend (before 11/13), at which point we can begin iterating on the final product using the 2-3 weeks we have left before the final demo day.

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