1. Introduction

1.1 The Motivation: Beyond Human Capability

For humans, horizontal movement is easy. Humanoid robots have recently advanced to human-level flat land traversing capabilities. By comparison, humans are significantly limited in vertical mobility. Humanoid robots have an opportunity to advance far beyond human capabilities in vertical mobility in the near future, and this would solve a myriad of complex problems.

1.2 Background

Researchers and engineers have been interested in the problem of robot vertical mobility for many years. Many have studied the problem by observing how it is solved in nature; an example of such an attempt, Festo’s BionicKangaroo, is shown in Figure 1.2.1 below.

Figure 1.2.1: Festo’s BionicKangaroo.

Most look at the problem of vertical mobility as a means for more efficient horizontal movement, because jumping can be an efficient way to move horizontally. Few have approached the problem as a way to significantly improve robots vertical mobility, which is a closer comparison to flying robots than horizontally moving robots. The few examples that have studied the problem of significant vertical mobility—such as Boston Dynamics’ Sand Flea Robot shown in Figure 1.2.2 below—have not found success beyond the prototype stage. What is missing in this problem area is an approach that focuses on extreme vertical movement using efficient, low-cost methods that are easy to reproduce. 

Figure 1.2.2: Boston Dynamics’ Sand Flea Robot.

2. Problem Statement

2.1 The Problem: Humanoid Robots are Bad at Moving Vertically

Robots that require vertical mobility typically fly. But this poses a problem for humanoid robots. Humanoid robots are typically very dense in order to fit all of their required components (battery, sensors, stability structures, etc). This density prohibits them from flying to augment their vertical mobility. Yet, superhuman vertical mobility is an important requirement for humanoid robots to succeed in the areas we need them to. Humanoid robots should be able to move from the ground to hard-to-reach areas repeatedly and with ease. This is a vital skill for many tasks, including 1) traversing rough or uneven surfaces or 2) reaching remote areas.

2.2 A Complex Problem

Vertical mobility for humanoid robots relies on jumping, or; exerting an amount of mechanical force that is multiple times greater than the weight the body that is doing the exerting. Mechanical force or power is typically limited by the physical trade-off between force and velocity. This necessitates a power-amplifying mechanism to enable an acceleration large enough to execute a successful jump exhibiting the phases shown in Figure 2.2.1 below.

To repeatedly execute successful jumps, autonomous robots must be able to:

1. Reach high accelerations,
2. execute multiple jumps without human intervention, and
3. execute multiple jumps with little degradation over time.

Figure 2.2.1: Jumping phases.

Achieving the above capabilities requires a powerful robot with a specific type of coordination in which the robot can identify and otherwise correct itself to a jumping position no matter how it lands. The robot must also be physically capable of withstanding repeated impacts, with the mechanism remaining stable enough to provide predictable output between iterations.

3. Mechanism

3.1 The Path: Mechanical Advantage

To succeed against the problem described in Section 2, a mechanism must maximize mechanical advantage to enable a larger, almost disproportionate jump height response. Specifically, the mechanism must be optimized to output maximal vertical force. A mechanism that can output a vertical force multiple times its weight must be a significant force multiplier. Specifically, it must have a mechanical advantage greater than 1, but more likely in the range of 3-5. The classic example of a force multiplier is a pulley system, shown in Figure 3.1.1.

Figure 3.1.1: Pulley system.

3.2 A Successful Mechanism

3.2.1 Inspiration from Nature.

Our chosen mechanism will utilize the flea (order: Siphonaptera) as a source of inspiration:

Figure 3.2.1.1: Kinematic breakdown of flea jumping mechanism.

Flea jumps are powered by a spring-like mechanism in the leg structure that leverages significant mechanical advantage to enable force-multiplying jumps to launch it many multiple times its height. The force from flea jumps start from the tarsus (the lower hind leg) and launch using the contact between the tibia (calf/foot) and ground.

Our mechanism will be similar to the one pictured above, with some added constraints:

1. Our mechanism will make use of guide rails, so the main focus will be maximizing vertical force output.
2. Our jump-height to mechanism-weight ratio will be much smaller than the flea’s, which can be upwards of 200.

3.2.2 Description of Proposed Mechanism

The mechanism will be composed of 2 systems: (i) the jumper and (ii) the guide rail. This will restrict jumping to 1 degree of freedom (DOF); vertical. The guide rail will be composed of top and bottom plates held together by 2 vertical rails. The top and bottom plates will be held in place with the bottom plate resting on the ground. Our mechanism with sliding output, henceforth referred to as the “jumper”, will be constrained between the top plate, bottom plate and guide rails. At a high level, our initial jumper mechanism design comprises 8 links with a cam device driven by a DC motor as one of the links. This cam-DC motor link will in turn drive a torsion spring. This torsion spring will be connected through the linkage structure which will multiply the force inputted by the cam-DC motor link. (See Section 5 for a detailed description of our mechanism)

4. Proposed Scope

The biggest technical hurdle that must be overcome to reach the above objective is creating a mechanism that produces a large force multiplier effect while maintaining the structural integrity required for repeated, autonomous jumps. Our project scope is constrained to focus on this particular challenge by limiting other, compounding challenges:

• We will limit our mechanism to one DOF (vertical). This will be achieved by using a guide rail system that will further ground our jumper mechanism.
• The mechanism will be designed to return to a singular base state after every jump to enable quick position reset. The mechanism superstructure and quick operational behavior will work in tandem to enable such a state.
• The sliding jumper in our mechanism will be designed to house as few electrical and hardware components as possible to minimize weight. We plan to house only a DC motor and linkages within the jumper structure, with all other required electronics held outside of the system.

4.1 Initial Design Concepts

We will develop various mechanism design concepts that utilize unique kinematic approaches to achieve the goals defined in Section 2 and our stated operational scope of 1 DOF in the translational vertical direction. We will test these design concepts in CAD by conducting force and acceleration analyses on our design concepts using FEA to improve each design and rule out designs that are insufficient. We will focus most closely on the load-bearing “foot” link and the spring-loading link aspects of the mechanism design due to their importance in achieving the high force and acceleration required.

4.2 Prototyping and Fabrication

4.2.1 Developing the Sub-Components

After finding a winning mechanism design concept using FEA, we will enter the fabrication phase. We plan to iterate often, so we will initially create semi-functional prototypes to test specific sub-assemblies. We will make sub-component prototypes only out of materials and processes that we can quickly iterate on; laser-cut acrylic or wood, structurally optimized 3D-printed elements and off-the-shelf components such as linear bushings. For example, we will build, test and iterate on only the CAM-DC motor link until it is sufficiently powerful and strong. We will do this with every sub-component before creating the full assembly.

We will initially create non-functional prototypes, moving to functional prototypes after ensuring desired and predictable motion output. We will evaluate the success of each design by measuring actual forces and distances that the device produces and overall robustness in operation. Material choices will likely change through both the initial design process and prototyping stage, as will link lengths and geometries. 

The most potentially-gating part of our project will be the superstructure and its components—with our implementation of vertical guide rails, we may need to introduce metal components into our design to support our mechanism and counter any moments that it may generate in order to maintain a 1 DOF condition. This may require machining, with a remote chance of us looking at potential production lead times depending on the complexity of our designs. Machined components may also be necessary for load-bearing components in our linkage system depending on the results of our structural analysis.

4.2.2 Critical Technical Milestones

When we are satisfied with each component and sub-assembly, we will assemble them into a full mechanism. We will continue to make modifications at this stage, but they will be modifications to sub-assemblies rather than full design iterations. 

We will continue iterating on the mechanism assembly until the following 2 critical technical milestones are reached:

• Milestone #1: Reproducibly achieve a vertical jump height of at least 2 feet.
• Milestone #2: Complete at least 3 autonomous jump and land cycles without failure.

5. Preliminary Design

The linkage mechanism shown in Figure 5.0.1 depicts both its jumping and loading state. The mechanism centers around a cam device driven by a DC motor (link 8), which drives a torsion spring (connected by links 4 and 2). The stretched torsion spring stores energy, and due to the legs compressing (links 1 through 4), the angle between link 6 and 1 compresses. Once the cam passes the torsion spring, it snaps back to its original jumping state and triggers the jump. Link 7 is the output link and will be attached to the mounting plate of the rail system, which serves as ground. Note that more torsion springs can be added at other joints to increase the stored energy for better jump height. There are two half-joints in this linkage: the contact between the cam and spring and the contact between link 1 and ground. The mechanism is intended to stay Grashof, with link lengths to be determined through iterative computational methods due to the complexity of the system. The mechanism is also intended to have 1 DOF according to the Gruebler equation below:

Figure 5.0.1: Kinematic diagram for cam-loaded linkage mechanism.