1.2 Kinematic Analysis:
Mobility Calculations/Grubler Equation:
Ground: L1
Motor Pulley: L2 (g: O2)
Geneva Driver via belt: L3 (g: O3, h: A23)
Slider Coupler via bearing: L4 (f: B34)
Slider Block via bearing: L5 (g: O5, f: C45)
Geneva Follower via bearing: L6 (g: O6, h: D36)
Right Pulley via belt: L7 (g: O7, h: E67)
Left Pulley Gear via gear: L8 (g: O8, h: F68)
Left Pulley via belt: L9 (g: O9, h: G89)
Key: g = full joint to ground, f = full joint, h = half joint (belts/gears only remove 1 additional DoF)
9 links, 2 full joints between components, 7 full joints to ground, 5 half joints (belts/gears) between components = 1 DOF (M = 3(L-1) - 2J1 - J2 = 24 - 18 - 5 = 1)
Kinematic Analysis for Wiper:
The mechanism can be broken down into two main components, one of which is the wiper, modeled as a slider-crank. In Figure 2, we have plotted the linear position of the wiper along with its linear velocity and linear acceleration. The crank (l2) has a length of 0.0285 m, the coupler (l3) is 0.130 m, and the offset is 0.0283 m. Using these linkage lengths and the vector loop solution, we were able to obtain the position, velocity, and acceleration plots over one full cycle of the driver, which also serves as the input for the Geneva mechanism.
Mechanical Advantage of Slider Crank:
This plot shows the mechanical advantage of the wiper with respect to the driver. The minimum magnitude of the mechanical advantage is approximately 1. Considering the gear ratio of 3.33:1 from the motor to the driver, this indicates that there is sufficient force amplification to continuously drive the wiper along the glass during the cleaning cycle. The mechanical advantage increases significantly near the points where the direction of motion changes (velocity of slider approaches 0), indicating higher force transmission in those regions.
Mechanical Advantage of the Pulleys:
Nout = 100, which is the teeth on the pinions turning the pulleys. Nin = 30 for the driver of the pulleys.
mv = ⍵in / ⍵out = (⍵in / ⍵out)-1 = (Nout / Nin) = (100 / 30) = 3.33
The mechanical advantage signifies that the output is 3.33 times the input and therefore the climbing mechanism will be efficient in pulling its weight.
Kinematic Analysis of Pulleys:
These plots correspond to the angular position, velocity, and acceleration, as well as the linear velocity and acceleration, of both the left and right pulleys. The left pulley has a starting position of 180 degrees, while the right pulley has a starting position of 0 degrees. These plots represent spinning the driver counterclockwise (CCW), resulting in the left pulley rotating CCW and the right pulley rotating clockwise (CW), which raises the mechanism. The results are plotted over four complete rotations of the driver, which correspond to one full rotation of the Geneva follower and thus one complete rotation of each pulley. As seen in the graphs, due to the Geneva mechanism, for each complete rotation of the driver there is approximately a quarter rotation of the pulleys, which is shown by the step-like nature of the angular position plot. Since the pulleys rotate in opposite directions, they have angular velocity and acceleration that are equal in magnitude but opposite in sign; however, given the 1:1 gear ratio from the follower to both pulleys, they have the same magnitude for angular and linear velocity and acceleration.
Animations:
Velocity:
Acceleration:
Ideal Motion:
As shown in the graphs, the ideal motion profile for the slider-crank is a smooth linear reciprocating motion, allowing for effective cleaning of the window. To ensure that a full cleaning cycle is completed before the mechanism raises (or lowers), the Geneva mechanism converts continuous motion into periods of motion and dwell. Thus, the mechanism only changes position after a full cycle of the wiper (slider-crank).