5. Kinematic Analysis (ALAG)

As stated in the initial project proposal, analysis that will need to be performed prior to the fabrication includes the following. We need to understand the motion profiles of the linkages as well as the rotary motion from the base to the claw. Furthermore, we will analyze the force profile of the grabber, the arm’s geometry/dimensions, and overall design via SolidWorks simulation. We would like to use the minimum amount of materials so the arm can take up as little space as possible, and we need to analyze the rotation of the base with respect to the other components such as wires. 

Analysis was done using Solidworks. An entire assembly was made of the mechanism, including the motor. A common input can be applied to the modeled motor, which is the input theta. From there, position of a point, velocity of a point, and force of a point can be found. Solidworks can export the data to Excel spreadsheets, which are linked below. 

Analytically finding the position profile of the claw is just a sanity check, as this position profile is what drove our entire brainstorming process, and the prototyping stage was to match the position profile of the prototype to the expected. We set the origin for our analysis on the first joint on the base frame from the ground up, which is represented by (0,0) on the graph below for the position of the grabber. Here, the x- and y-positions of the claw are shown for our mechanism in inches. The grabber goes from -0.5 in to 3.25 in, in the y-direction. This makes sense because the claw moves slightly below our origin joint in the most extended position. Then, when it contracts upwards, it moves 3.25 inches above the joint of reference. For horizontal movement, the claw moves on the right side up to 6 in, then crosses through 0, and up to -6 in on the left side extended reach. The position of the claw graphed is shown below on the left. Additionally, we decided to graph the linear claw displacement as a function of the input angle, ranging from 0° - 360°, shown below on the right. The blue curve represents the x-position, the orange curve represents the y-position, and the gray curve symbolizes the total displacement of the grabber. This plot agrees with the one we have above since the blue curve starts at 6 in (the right side reach) and then moves to -6 in (the left side reach). The orange curve shows that as the claw moves from right to left, it starts at a position slightly below the origin, climbs back up as the arm contracts, and then lowers back to the same position for the extended reach on the other side.  Lastly, the gray curve shows the square root of x2 + y2 and shows the overall positive displacement of the grabber. 

Shown below is our graph for the velocity of the grabber versus the input angle. The x-direction of the claw’s velocity is represented by the blue curve, the y-direction of the claw’s velocity is detailed by the orange curve, and the overall magnitude is shown by the gray curve. From the plot, we can see that the maximum y-velocity is around -5.8 in/s, the maximum x-velocity is about -6 in/s, and the maximum magnitude is approximately 9 in/s. Additionally, we can see that the claw stays within a reasonable range for its entire transversal. This means that the arm will maintain control of the object it has in hand.

Below is our plot of mechanical advantage versus the grabber x-position to intuitively see the strongest and weakest parts of our design. We can see that there are two asymptotes on the graph that converge to infinity; these correspond to when the grabber is in the most extended left and right side positions. These go to infinity because the arm temporarily stops while the input is continuously running. In this situation, anything over zero will go to infinity. Furthermore, we can see that the weakest point of our design where the mechanical advantage is 0.5 is the path that the grabber takes when traversing through the origin. This is okay with our design because we are not carrying an extremely heavy load through these points.

Below is a graph of the upward force of the grabber versus its x-position, which matches up nicely with our graphs in the position analysis. From the math, at the extreme positions of -6 in - 6in, this analysis shows us that our mechanism can lift a large amount of weight.  This is promising because the extreme positions are a weak spot in our design. The absolute minimum of this graph is around 10 lbs, which is approximately 3 in away from the center. This means that if a higher force is applied, our mechanism could get stuck here because the torque would not be sufficient to overcome that force.