1.1 - Project Proposal
Introduction
Rock climbing is a fun and physically demanding activity that requires strength, agility, and balance from the climber, a practical and reflexive understanding of physics. The forces at play, such as gravity, friction, and torque, challenge climbers to strategize their movements to scale vertical and overhanging surfaces. However, what if a robot could emulate these movements and successfully navigate rock climbing environments? The development of a rock climbing robot is not only an exciting challenge but also has significant practical applications. Such robots could be used for exploration in hazardous environments, search-and-rescue operations, and maintenance of structures in hard-to-reach places, and could revolutionize robotics in areas such as construction, space exploration, and disaster response.
Problem Statement
Our problem takes a simplified simulation of the complex nature of rock climbing. By reducing the problem to a predictable pattern, as depicted in the below figure, we can begin to construct a mechanism that can autonomously climb. Specifically, our proposed problem involves traversing a positively inclined board with standard indoor rock-climbing holds occurring in an alternating 2-1 pattern. We propose that by maintaining a consistent horizontal spacing (dimensions D2) between the holds and consistent vertical spacing, we can simulate a basic arrangement of rocks and keep the problem restricted enough to be realistically traversable by planar robot mechanisms.
This problem requires a complex motion profile due to both the physical arrangement of the holds as well as the fact that the robot needs to support its own weight. The motion profile of the climbing mechanism must be such that it is able to achieve purchase on the rocks without colliding with the board on which they are mounted. Additionally, the motion profile must either be adjustable or constructed in a way that it can account for uniform vertical spacing between rocks (dimensions D).
Finally, the velocity and force profile of this climbing mechanism must provide the necessary force and stability in order to support the weight of the robot without sacrificing stability.
Proposed arrangement of rock-climbing holds
Mechanism
Our idea for the mechanism will be some kind of walking linkage which will likely be a combination of linked 4-bars, to allow use to evaluate the kinematics based on the principles we learned in class.
We can have a 4-bar that gives us our desired motion profile, to which we will affix an arm with a hook of specific geometry and length such that our motion profile smoothly translates to end effector position which properly travels from hold to hold.
Since we are powering our joints with a motor, our input ideally will be a crank with a full 360 degree ROM which should simplify the code and design.
The robot will incorporate a set of wheels at the bottom of the climbing plate, enabling it to roll along the back wall while pulling itself upwards. The wheels will be designed to traverse around holds, ensuring mobility even when navigating between the rails.
To maintain balance in the robot, our idea is to have the setup be one arm in the middle on a separate timing, while the two outer arms have identical linkages and are on the same timing. This means that the outer arms would grip a hold, pull the robot up, and then the middle arm would go up and grip while the outer arms disengage.
Our hook will be similar to a spring hook mechanism that will allow it to securely latch onto the rocks. It will include a small spring-loaded spring latch that will put against the rock hold in the first pass and then hook onto the rock on the way back, giving us a simple toggle system.
Step-by-Step Motion of the Robot
Initial Hold Position:
The robot starts with its two outer arms hooked onto the climbing holds, supporting its weight.
Middle Arm Extension:
The middle arm moves forward and extends using its four-bar linkage to hook the next available hold.
Middle Arm Retracts:
Once the middle arm successfully grasps the hold, it retracts, pulling the robot up and supporting its weight.
Outer Arms Extension:
The outer arms rotate and extend to reach the next set of available holds above the previous position.
Outer Arms Retract:
Once the outer arms successfully grasp the hold, it retracts, pulling the robot up and supporting its weight.
Cycle Repeats:
The process repeats as the robot continuously climbs higher by alternating between middle and outer arm engagements.
This cyclic motion ensures the robot maintains stability while efficiently ascending the rock-climbing surface. A great degree of care and clearance verification will be required to ensure that the cyclic motion lines up with the holds without issues.
Four-Bar:
Step 1: The crank (input link) rotates when powered by a motor.
Step 2: This causes the coupler link to move in a controlled arc.
Step 3: The follower link lifts the gripper, allowing it to reach the next rock hold.
Step 4: Once the grip is secured, the motion sequence shifts to the other arms.
Proposed Scope
For this project, we aim to complete a robot with the full functionality of climbing a vertical wall with certain conditions. We will need to perform mobility, position, kinematic, and velocity analysis using tools such as MATLAB, Python, and SolidWorks as a visualization technique. We will design a sample rock climbing wall using 3D printed holds. Additionally, our team will laser cut the linkages and the chassis and we will 3D print the mounts needed for the motor. We will require a motor controller and an Arduino to be able to control the linkages autonomously.
Stage 1 (Complete by project deadline)
For the first stage, the robot will be able to climb a vertical wall with the horizontal distance between rocks and the vertical distance remaining constant. The motor will be calibrated for smooth movement of the joints and the robot will autonomously climb the wall. As an added interest to members of our group, ANSYS could be used to run FEA simulations to show where failures would most likely occur on the robot.
Stage 2 (Ambitiously complete by project deadline)
After the first stage is accomplished, we plan on making the vertical distances between the rocks have a a variable spacing, adding complexity to the robot by incorporating a linear slide into the fixed link to vary the gait length.
Stage 3 (Complete as personal project after the class)
After the second stage is accomplished, we plan on using vision sensing and a corresponding algorithm that would automatically adjust the robot geometry to match the spacing of the holds on the wall. If time permits, our group members will perform hand calculations using a MATLAB or SOLIDWORKS truss solver to validate whether the motor has sufficient power to perform the motions, given the mass of the robot and mechanical advantage of the links.
Preliminary Design
The following schematic was used to model a single arm for the proposed mechanism:
Gruebler’s Equation:
Gruebler’s equation can be used to find the degrees of freedom of our mechanism.
Since two of the arms will have the same timings along with the middle link that is independent, it leads to a total of two degrees of freedom for the arms of our robot.
Grashof Condition
We can verity that our proposed linkage allows for at least one link to make a full rotation by ensuring that it complies with the Grashof condition which states that the following condition must be met:
The proposed lengths of our links are as follows:
Link | Length |
Link 1 | 105 mm |
Link 2 | 112.5 mm |
Link 3 | 72.83 mm |
Link 4 | 37.5 mm |
Longest link (L) : 112.5 mm
Shortest Link (S): 37.5 mm
Other two links (P and Q): 105 mm and 72.83mm
Applying the Grashof Condition:
Which is satisfied, meaning is a Grashof linkage.
Proposed Hook Design: