16.1 - Project Proposal
Introduction:
Navigation of complex terrain is crucial for robotic vehicles used in rescue and exploration. In these situations, vehicles need to be able to climb over steep ledges and into small crevices. There is a tradeoff between these two abilities depending on the diameter of the vehicle’s wheels, as large diameters can climb over obstacles while small diameters can fit into tight spaces. Our robot will contain a mechanism to increase its wheel diameter to climb edges and decrease the diameter to duck into small spaces. This effectively solves the problem and creates a more robust system for vehicles being used in rescue and exploration
Description of the Problem:
The problems faced in this project lie in the flexible geometry, seamless transitions, and complex motor/force profiles needed to change the radius of a wheel under load. The wheels need to be able to change their sizes without compromising traction or drivability. These morphological transitions need to be smooth and adaptive without sacrificing dynamic stability. In order to accomplish this, complex position and force profiles will need to be drafted. The position of our output link which controls wheel radius needs to be contained within the bounds of the smallest desired radius and the largest desired radius. Additionally, enough torque needs to be delivered so that regardless of the current rotational position of the wheels, they can be stably opened and closed.
Description of a proposed mechanism that could solve this problem:
In order for our wheels to be able to expand and contract, we plan to use four bar slider crank linkages along with a rack and pinion system that will control the wheel radius in a manner similar to umbrella operation. One challenge will be designing our mechanism to withstand the forces it will be subjected to without the wheel collapsing. This will need to be done with a combination of linkage design and physical stops.
AI generated Model of Adjustable Wheel
Proposed scope of work for final project:
For the scope of this project, our objective is to design adjustable wheels for a robotic vehicle. These adjustable wheels will be capable of changing their radii based on the need for the terrain that the robot is traversing to perform any rescue or exploration.
Our target for this project is to design and implement variable-radii wheels which will increase radius up to 40% approximately when installed on a robotic vehicle like that from build assignment two. We are planning to use a joystick to control the radius change.
This design includes linkages and mechanisms like slider-crank mechanism. Thus, scope of the project will also include preliminary kinematic analysis of our design like DOF calculation, understanding the mechanism and its constraints, position/velocity/acceleration analysis as needed to ensure we will have proper range of motion to achieve our design goals. In addition, we have motors as part of design, so we will need to analyze force/torque and speed profiles for the motor.
Finally, we can proliferate this design idea to larger scale by using various sensors which can detect obstacles, tight spaces, and diversity of terrains, and then change the radii autonomously based on the feedback from each sensor to overcome the difficult terrain.
Preliminary design ideas:
This project proposes a novel design for a transformable wheel robot capable of adapting to varying terrains. The core mechanism relies on a centralized rack-and-pinion system that drives a multi-blade linkage structure, allowing the wheel to dynamically change its diameter. This preliminary design focuses on ensuring transmission efficiency, strict symmetry of linear motion, and overall structural robustness.
As illustrated in the overall design schematic, the driving module utilizes an integrated internal electric motor to drive a central gear. This gear meshes simultaneously with two parallel rack gears (the top and bottom rack gears). As the central motor rotates, the pinion drives the top and bottom racks to generate synchronized linear motion in opposite directions. These two racks are connected to the left and right motor/reduction housings and main support shafts, effectively acting as sliders that directly push and pull the end-effector gripper/wheel assemblies.
The core advantage of this design is its ability to precisely and linearly convert the rotational motion of the motor into synchronized translational input for both sides of the mechanism. This rack-and-pinion setup ensures high consistency in the transformation actions on both the left and right sides without generating unwanted lateral loads, providing a highly stable mechanical foundation.
At the wheel's execution end, we employ a highly efficient multi-blade design concept. Through the push-pull action of the internal mechanism, the wheels can smoothly transition between a shrink mode (with an external diameter denoted as Dshrink and an expand mode (denoted as Dexpand).
Crucially, as depicted in the kinematic sketch, the black slider and the red shaft (which directly connects to the DC motor) are designed to slide relative to each other. Because of this relative sliding capability, the morphological transformation of the wheel and the rotation of the wheel (driving the robot forward or backward) operate as two completely independent mechanical systems. Therefore, the kinematic and Degree of Freedom (DOF) analysis presented herein applies strictly to the transformation mechanism, isolating it from the wheel's rotational driving dynamics.
For the transformation mechanism, the expansion of a single blade is controlled by a precise slider-rocker mechanism. The schematic defines the geometric dimensions of the links (a, b, c, d, etc.) and the kinematic angle parameters 2,3. The linear displacement x transferred from the central rack directly alters the relative distance between the base and the slider, driving the coupler to lift the external rocker.
To verify the deterministic nature of this motion, a DOF calculation was conducted for the end-effector linkage system. Setting the number of links as L=6, the number of lower pairs as J1 = 7, and higher pairs as J2=0, the Kutzbach-Gruebler criterion yields:
M = 3(L-1) - 2J1 - J2= 15-14 = 1
The result M = 1 demonstrates that the end-effector linkage has exactly one degree of freedom for wheel transformation mechanism. This mathematically confirms that once the central rack-and-pinion mechanism provides a specific linear displacement input, the expansion angle of the wheel blades—and consequently the final working diameter of the wheel—is completely deterministic and precisely controllable.
In conclusion, the implementation of a central rack-and-pinion structure provides high stiffness and accuracy for the transmission system. Coupled with the 1-DOF end-effector linkage and the decoupled rotational drive design, this architecture ensures that the robot can execute smooth, stable, and perfectly symmetrical morphological changes when navigating complex, unstructured terrains. This highly deterministic kinematic profile provides an exceptionally reliable hardware foundation for the future integration of automatic control algorithms.