1.1 Initial Proposal

Introduction: 

Walking mechanisms are an extremely popular concept in robotics, and their development has seen significant progress in recent decades. Engineers have got the process of walking down to a science, but the same cannot be said for climbing. If you want to stop a walking robot in its tracks, all you have to do is present it with a wall. In our project, we hope to delve into the challenges facing climbing robotics and explore new modes of vertical mobility.

Description of Problem: 

We plan to develop a mechanism that is able to climb and pull itself up between two parallel walls. This will require precisely timed motions that distribute forces evenly throughout the robot, resulting in a steady movement upward. In order to keep the robot stable as it scales the walls, large friction forces must be employed. In order to obtain this friction, distributed loads must be applied. A simple joint cannot easily provide such a load, and so it is necessary that we utilize more complicated linkages in our design.

Description of Proposed Mechanism:

To solve this problem, we are going to implement a similar mechanism to what is found in question 2 of homework 2. We will use a 4 bar mechanism that has a ternary link to allow for a flat, vertical motion that allows for optimal time to climb up the wall without causing compression stress on the mechanism. There will be 3 sets of two legs with each set having the same movement timing on either side. The timing for each set will be offset to allow for continuous contact with the walls so that the robot is not at risk of falling. All three sets of legs will be powered by a singular motor that will connect to a gear train so that all 6 legs can have movement. The legs will then have a spring actuator to allow them to conform to the wall, further reducing the compression stress on the leg mechanisms. 

Preliminary Design:

Figure 1 illustrates a kinematic diagram of the desired leg movement. The goal is for there to be 6 total configurations of the illustration below that will be controlled at joint L1. The kinematic diagram illustrates the path to be followed by the ternary link L3. The path in red demonstrates points of contact between the ternary link and surface of the wall. This path idea is further supported in Figure 2. 

Figure 1: Kinematic Diagram of Proposed Leg Movement

Prototype 1 Initial Parameters

L1 = 32mm

L2 = 16mm

L3 = 32mm 

L4 = 20mm

Ternary LP = 40mm

Gruebler’s Equation

M = 3(L-1) - 2J1  -  J2

M = 3(4-1) - 2(4) - 0

M = 9 - 8

M = 1

Our 4-bar linkage system has 1 degree of freedom.

Grashof Condition

S + L ≤ P + Q

16 +32 ≤ 20 +32

48 ≤ 52

Since this mathematical statement is true, at least 1 link in our linkage system can make a full rotation.

Matlab Plot of Path Followed

The plot in Figure 2 is adapted from Problem #2 in Homework #2 using our chosen link lengths and an angle of 60 degrees between L3 and LP. If units are in mm, then the contact with the wall (The x-axis) is shown to last for approximately 15 mm. This value could be increased by scaling the link sizes or using springs to increase the contact threshold (Effectively raising the x-axis in the plot by allowing for longer contact without stalling).

Figure 2: Matlab Plot of Path Followed

Gear Train For Movement

The gear train will be made up of 10 gears, 6 which are connected and giving mobility to the legs, and 4 gears to connect them all together. The setup can be seen below in Figure 3. One of the gears will be motorized and connect to a gear on the other side to create the same motion, just inverted. The smaller connection gears will allow for each leg on each side to all have the exact same rotation, the initial positions of the legs will be the only thing that is changed in order to have a leg on each wall at all times. 

Figure 3: Gear train sketch

Proposed Scope of Work: 

While we want to explore new modes of vertical mobility including uneven terrain, our project will only be focusing on even terrain during the semester. Specifically, we will only be focusing on traversing even vertical walls with a known distance in between the walls. We only foresee us completing this specific section of our solution as part of the final project. Prior to fabrication, we will need to perform analysis on our 4 bar linkage system to determine our linkage path, maximum force with the wall, required force to enable climbing, and contact time with the wall. Analyzing these components should give us the calculations we need for the scope of the final project. However, to fully address our problem, we would need to analyze how all of the previous components change with uneven/unknown terrain.