Modular Robotics Connection Scheme

Second iteration of “bank vault” prototype actuated by hand

Actuation demonstrated in CAD assembly

Foreword

This is the capstone project for my Bachelor’s degree in mechanical engineering at Northwestern University. My team is composed of 8 members. The work I am showcasing are the portions I have greatly contributed to. I intentionally excluded designs I didn't lay the groundwork, that other teammates contributed more to, aiming to highlight my own skills and knowledge. More specifically, the core design featured on this page was a product of my ideation. This design was among 2 of 4 prototypes that had been chosen to further develop based on the evaluation of our first iteration prototypes. My teammates contributed to revisions in the second iteration of the design.

Mission Statement

To develop a modular robotic system for constructing infrastructure on extraterrestrial bodies through the reconfiguration of robotic modules into high-strength structures such as manipulator arms and cranes. These modular robots reduce the payload weight on spacecraft by reusing the same set of modules for different applications. They also facilitate rapid repairs, being capable of hot-swapping damaged modules instead of replacing entire machines. Our end goal is to design and construct a tabletop prototype capable of transforming into different crane configurations and withstanding static loads in a cantilever arrangement.

Background

Our clients, Ping Guo, an Associate Professor of Mechanical Engineering at Northwestern University, and Kojo Welbeck, a PhD student studying robotics at Northwestern University, approached us with the challenge of designing a modular robot system capable of reconfiguring into different geometries to fit any need. The clients gave our team the freedom of choosing which area of interest to design for.

Our team chose a project focused on extraterrestrial applications, driven by the unique advantages of modular robots in space. In space, obtaining new machinery or parts is challenging compared to Earth, where rapid, global shipping is available. Modular robots address this challenge effectively. Unlike traditional machines requiring specific parts for each component, modular robots are self-similar and can self-repair in harsh environments, ensuring continuous functionality even if a unit is damaged. Additionally, their reconfigurability reduces payload requirements, lowering transportation costs by replacing multiple specialized tools.

For the most part, the use of robots on extraterrestrial bodies have been largely been limited to exploration rovers. Our research uncovered that a number of research groups had developed modular robots for the purpose of exploration and traversal of planets’ surfaces. However, the use of modular robots in the establishment of base stations and habitats has remained largely unexplored.

Recognizing an opportunity to fill this void, we set our eyes on developing modular robots that aid in the construction and maintenance of infrastructure in space. We do not intend for the modular robots to form into a final, static form such as the frame of a building. That would be expensive and an under-utilization of their capabilities. We envision our system of robots as the building blocks of specialized tools. For example, it could transform from a crane to a frame for a 3D printer gantry and then to the frame of a mining conveyor belt. Next, we lay out the scope of our project:

We will not develop the software to intelligently control the robots.
The connections between modular robots are automatic, but the assembly of the robots themselves will be aided by humans, as self-assembly is a Herculean challenge in itself.
Our design will be for a tabletop version, rather than at the scale required for the construction of large infrastructure

Example Applications for Modular Robots on Extraterrestrial Bodies (from left to right: 3D printer arm constructed from modular robots, modular robots reconfigured into a crane

The demonstration used to measure the success of our solution will be the individual steps to assemble a structure from existing parts. Hence, our demonstration will be limited to the mechanical capabilities of an assembled system of modular robots. We are designing for the most strenuous type of infrastructure we want to support. We are not going to arbitrarily select a final infrastructure geometry to perform tests on. Instead, we will be examining the configuration that generates the most stress on the connection between two modules in an assembly of an arbitrary number of modules: a cantilever beam. Testing mechanical configurations will allow use to validate our system without making assumptions about the configurations the system will transform into.

The critical system we chose to focus on was the connection scheme. Connection strength was one of the highest ranking needs for our project, since the system of robots would be manipulating heavy loads and act as the supporting structure of tool attachments.

Needs and Metrics

The needs and metrics relevant to the critical system are listed in Tables 7 and 8. The remaining needs and metrics of the greater system may be related to the connection mechanism, but are so indirectly. We have designated the challenges that arise from the non-relevant metrics as secondary to the core quick attach and detach functionality we hope to achieve.

From the relevant metrics, follow the primary requirements: high strength, incorporation of physical auto-alignment features, adherence to a plug and play (compact and lightweight) architecture, and easy to manufacture.

Metric 3: Structural Analysis

We are configuring $N$ robotic modules into a cantilever beam configuration. The following calculations will determine the axial force and the shear force each connection between neighboring modules is required to withstand. We are only evaluating the worst case, which is the connection that sustain the greatest forces and bending moments.

Let's define our problem (refer to the force diagram). We have $N$ modules, each weighing $m$ units of mass. Let the acceleration of gravity on any planet be denoted by $g$. Say the length of each module is $L$ and that a module's weight is uniformly distributed across its length. An assumption we make here is that the modules are cubic geometries. Let $M_a$, $F_x$, and $F_y$ (moment about the fixed end, force in the +y-direction, and force in the +x-direction, respectively) denote the reaction forces at the fixed end of the beam. A force $F$ is applied to the free end of the beam. We know that the bending moment and shear force are at their peak at the fixed end of the beam. Hence, we will be focusing on the connection between the left-most module and the wall.

First, we will calculate the reaction forces. The total weight of the $N$ modules is equal to $Nmg$. The weight density (force per length) is equal to $w=Nmg/NL = mg/L$.

$$\text{Sum of forces in y direction: }0 = F_y - \frac{mg}{L}(NL)-F$$

$$\text{Sum of forces in x direction: }0 = F_x$$

$$\text{Sum of moments about fixed end: }0 = M_a - Nmg(\frac{NL}{2})-F(NL)$$

We determine that $F_x = 0$, $F_y = Nmg+F$, and $M_a = \frac{1}{2}N^2mgL + FNL$. Next, we examine the cross-section at the fixed end of the beam. Let $N_C$ denote the number of connection elements/fastener (for instance, pins or bolts) between neighboring modules and $\text{FS}$, the factor of safety. We will make the assumption that the fasteners equally share the shear force. Hence, the shear force on each fastener is given by

$$F_{\text{shear}} = \frac{\text{FS}(Nmg+F)}{N_C}$$

To calculate the axial force each fastener experiences, we will make the assumption that fasteners are placed near the outer edge of the modules and that the placement of the fasteners is symmetrical about the neutral axis defined in the problem above. Slight modifications to the following calculations will need to be made if these assumptions are invalidated. We will first consider the case where two fasteners are used, one placed $L/2$ above the neutral axis and one placed $L/2$ below.

$$\text{Sum of moment about point on neutral axis: }0 = M_a-F_{\text{axial}}(\frac{L}{2})-F_{\text{axial}}(\frac{L}{2})$$

$$F_{\text{axial}} = \frac{M_a}{L} = \frac{1}{2}N^2mg+FN$$

Next, we will consider the case where $N_C$ fasteners are used, placed symmetrically about the neutral axis.

$$F_{\text{axial}} = \frac{\text{FS}(N^2mg+2FN)}{N_C}$$

We note that the fasteners below the neutral axis will be experiencing compressive force, while the fasteners above will be experiencing tensile.

We estimate gravity on Earth to be $g = 10 \frac{\text{m}}{\text{s}^2}$. As per our design metrics, we estimated the length of a module to be $L=15$ cm and the weight of a module to be $m=10$ kg. We are designing for a load of $F=60 N$ at the free end and, say, a factor of safety equal to $\text{FS} = 1.5$. Let's say we are using $N_C=4$ fasteners. I will derive the expression for shear and axial force per fastener as well as the maximum bending moment, both as functions of $N$. The maximum bending moment is equal to $M_a$ in the force diagram but will be scaled by the factor of safety.

$$ F_{\text{shear}}(N) = \frac{1.5(1.5N+60)}{4} = 0.5625N+22.5$$

$$ F_{\text{axial}}(N) = \frac{1.5(1.5N^2+2(60)N)}{4}=0.5625N^2+45N$$

$$M_{\text{max}} = 11.25N^2 + 13.5N$$

For $N=4$, $F_{\text{shear}} \approx 24.8$ N, $F_{\text{axial}} \approx 189.0$ N, and $M_{\text{max}} \approx 234$ Nm.
For $N=5$, $F_{\text{shear}} \approx 25.3$ N, $F_{\text{axial}} \approx 239.1$ N, and $M_{\text{max}} \approx 348.8$ Nm.
For $N=10$, $F_{\text{shear}} \approx 28.1$ N, $F_{\text{axial}} \approx 506.3$ N, and $M_{\text{max}} \approx 1260$ Nm.

We can use these estimates as a rough guideline to evaluate the design of our proposed connection schemes. For mechanical connections, important considerations that need to be made are the strength of the material (ultimate tensile strength and shear strength) and the density of the material (which affects the modules' weights). Generally, we should aim to maximum the ratio of the ultimate tensile strength to the total weight of the mechanism. For a number of common metals, shear strength is roughly equal to 0.7 times the ultimate tensile strength. Hence, by maximizing this ratio, we are simultaneously maximizing the axial and shear force the connection can withstand. For electromagnetic connections, the magnets' pull force and the weight of those magnets are the most important strength factors. Likewise, we should aim to maximum the ratio of the pull force to the total weight of the magnets. Resistance to shear is largely generated by frictional forces for magnets. The larger the pulling (normal) force, the greater the shear force a pair can withstand. Of course, a surface with a higher static coefficient of friction will resist shear better.

Metric 4: Ease of Connection

We define automatic attachment and detachment as a mechanism that fixes two separate modules' faces together without external manipulation. This metric does not require that the alignment nor positioning of the two separated modules is automated; this step can be done by hand. It is, however, a requirement that the design of the connection mechanism offers auto-alignment features that allow for imprecise positioning of the two module's faces. This requirement arises from the phrase “with ease." Another consideration that arises from the ease of connection is the number of possible orientations that the faces can connect. For instance, if the faces must be orientated 90$^\circ$ relative to each other to connect, then the faces can only connect in two orientations. The greater number of orientations faces can connect, the greater the ease of connection.

Design

Iteration 1

The design of the prototype I conceived was loosely influenced from the locking mechanisms that bank vaults use. I wanted to mimic the motion outputted by a bank vault, the radial extension of pins/locks from a single source of actuation. Banks vaults typically use a complex gear train to achieve this motion. A central spur gear rotates smaller spur gears centered on a larger circle, which themselves are pinons actuating the linear motion of racks or, alternatively, the drivers of a slider-crank linkage. The mechanism described here was deemed to be inept for our project's needs for two reasons: the first was the small length to which the locks move out, and the second was the issue of compacting a number of gears and moving components into a small 15 cm circular face. We needed a mechanism that could achieve the same output through simpler means.

We arrived at the solution of using a cam plate, which negated the need for a complex gear train. The central idea was that a cam plate rotates in the center, causing the locks to extend or retract radially. In the design of the first iteration, modules' faces can connect in two orientations: 0$^\circ$ and 180$^\circ$. This is because the connecting module's face must be rotated 90$^\circ$ relative to the other module's face. The first iteration of this concept is shown in the following figure. Table 9 lists the unique parts that compose the assembly of a single connection face.

Iteration 2

Design changes between iteration 1 and 2 of the vault prototype can be seen in the next few figures and are described on a component bases in Table 11.

Significant loading conditions of two connected faces are shown in cross-sectional view in the figure below. The cyan and magenta outline the two faces coming together, and the dark blue outlines the lock keeping the faces together. The red force arrows are applied to the locks, and the yellow arrows are the reaction forces applied to the restraining arches of the faces. We use this information to inform manufacturing processes and material selection in the following section.

Manufacturing

The first and second iteration prototypes’ purposes were to validate that the design could fundamentally work. The main concern arose from the uncertainty that the cam followers would get jammed in their respective paths in the cam plate. If this were to happen, then the locking mechanism would require maintenance or external persuasion to unbind the cams followers, meaning that metric 4 is not met. For the purpose of validating basic functionality, we chose the quickest method of prototyping that could form the geometries of our design, 3D printing. We planned to 3D print all the parts in the bank vault prototype. We didn't anticipate any issues, given that the design featured no sharp overhangs and few places where support was needed. The manufacturing plans for future iterations are presented in Table 12.

Material Selection

Poly(lactic acid) or PLA was chosen as the printing material for the first and second iterations of the design because it's easy to print with and has a low cost, making it an excellent choice for rapid prototyping. The ability to quickly iterate on our designs is of the upmost importance in the early stages of our project's development. PLA also exhibits good layer adhesion and a relatively low melting point, facilitating precise and smooth printing. Material selections for future iterations are presented in the table below.

Strength Calculations

The following strength calculations are rough estimates meant to demonstrate that the design, if manufactured with stronger materials, meets the strength requirements outlined in metric 3. The cross-sectional area of the lock is equal to the lock's width multiplied by its thickness. That is, $wt=2 \text{ cm} \times 0.5 \text{ cm} = 1 \text{ cm}^2$. There are a total of $N_C=4$ locks per connection between two faces. The simplified load path for a single lock is shown in the figure above. Hence, the maximum axial force that can be withstood before one locks fail is given by the following equation.

$$F_{\text{max axial}} = \tau_{\text{max}} A_c = (0.5\sigma_{\text{max}}) A_c$$

$A_c$ is the cross-sectional area of a single lock, $\tau_{\text{max}}$ is the ultimate shear strength of the lock's material and $\sigma_{\text{max}}$ is the ultimate tensile strength of the lock's material. We are using nylon, which has an ultimate tensile strength of about 50 MPa, for the locks. The shear strength for 3D-printed nylon has not been determined in a laboratory setting. Generally, the shear strength of polymers are estimated to be half of the tensile strength. We calculate that the maximum axial force that can be withstood is equal to 2.5 kN.

In addition, we consider the case where the restraints fail instead of the lock. The restraints (the arches) have a cross-sectional area of $A_c=1.862$ cm$^2$. A normal force is applied to the restraints when the axial force pulls the two faces apart. The maximum axial force that can be withstood is given by Equation \ref{eq:fmax_axial_rest}.

$$F_{\text{max axial}} =(\sigma_{\text{max}}) A_c$$

Let's say we are going to use 7075 aluminum alloy, known for its high ductility, strength, toughness, and resistance to fatigue, for the restraints. The alloy is a common material used for aircraft structural parts and highly machinable. For aluminum alloys, the ultimate shear strength is approximately equal to 0.65 times the ultimate tensile strength (UTS). 7075 aluminum's UTS is equal to 572 MPa. We calculate that the maximum axial force before the restraints fail is equal to 106.5 kN.

Let's compare our results to the axial strength metrics we aim to meet. For $N=10$, $F_{\text{axial}} = 506.3$ N. Our design for the locks and the restraints surpasses that goal. Hence, we can say with confidence that the bank vault design meets the axial force strength requirements.

Next, let's calculate the maximum shear force the vault prototype can withstand before failure. The load path for the locks is the same for the two locks located on the neutral axes. Hence, the maximum shear force the locks can withstand in pure shear is the same as the maximum axial force per lock. The load path for the restraints, however, is different from the case of pure axial loading. In the worst case orientation, only the restraints on the neutral axis take any of the load. However, instead of a normal force being generated perpendicular to the face, a shear force is generated parallel to the face (see figure below). Again, the cross-sectional area of the thinnest section of the restraints is equal to $A_c=1.862$ cm$^2$.

Hence, the maximum shear force that can be withstood by the restraints is given by:

$$F_{\text{max shear}} = \tau_{\text{max}} A_c = (0.65\sigma_{\text{max}}) A_c$$

Assuming, again, that the restraints are made of 7075 aluminum alloy, we calculate that the maximum shear force before the restraints fail is equal to 69.5 kN.

Let's compare our results to the shear strength metrics we aim to meet. It's important to note that the sample calculations for shear force in the structural analysis need to be modified in order to be accurately compared to our design. Previously, we made the assumption the fasteners or locks are placed symmetrically about the neutral axis. However, in the worst case orientation, two of the fasteners lie on the vertical axis, while the other two are placed symmetrically about the neutral axis. Hence, the locks at the top and bottom of the circular face are taking a majority of the shear force. The modified shear force equation is given below.

$$F_{\text{shear}}(N) = \frac{1.5(1.5N+60)}{2} = 1.125N+45$$

For $N=10$, $F_{\text{shear}} =56.3$ N. Our design for the locks and the restraints surpasses that goal. Hence, we can say with confidence that the bank vault design meets the shear force strength requirements.

Validation of Functionality

The intended operation of the vault design is as such: once two faces are touching, a disk cam is rotated. This pulls a pin along the slots in the cam. The pin is attached to locks, which are constrained by linear guides. This allows the locks to move radially inward or outward. Moving the locks outward causes the locks to slide into slots (within notches) on the opposing face. This locks the faces together. The cam can be rotated the opposite way to retract the locks and unlock the faces. All the motion occurs in the same plane.

The notches that house the locks are located such that they fit into indented portions of the opposing face. These indented portions are larger than the notches, which successfully creates a self-locating mechanism for the two faces to interface. Therefore, even if the two faces do not meet at the correct orientation, they will orient themselves as the faces get closer together.

The vault functions as expected, but the fluidity of motion should be improved in future iterations. Currently, the system experiences occasional binding. While rotating the cam, the pins bind against the cam, which results in the whole system freezing. In future iterations, this could be eliminated by creating smoother surfaces for the pin-cam interaction. This could be achieved by sanding the PLA, using needle bearings around the pins, or using a smooth surface finish on a metal such as aluminum.

Future Work

The capstone class is a two quarter sequence, and I have not yet taken the second part of the course. Next quarter, we plan on reconstructing the connection scheme using higher fidelity materials and testing the strength by loading weight onto the faces. We also plan on undergoing another full product development cycle for the controls and actuation of the modules. This includes the development of a hinge, turntable, or rotatory joint system, as well as basic software to command the motors. The software implemented for the actuation is intended to only be for teleoperation control.