07.1 - Project Proposal
1. Introduction
In our present world, we have many different modes of transportation: drones, bikes, cars, trucks, and planes. However, our current mobility devices rely on wheels, which are efficient on flat and firm surfaces; they struggle in soft and uneven terrain.
In contrast, some organisms move gracefully across irregular terrain using legged motion. Inspired by this biological mechanism, engineers have explored systems like Theo Jansen’s Strandbeest linkage, which replicates the walking motion of legged animals. These mechanisms offer potential advantages in environments where wheels fail.
These challenges emphasize the need for alternative locomotion mechanisms that can adapt to irregular terrain. We need a mechanism that more closely imitates the walking gait of a biological organism, which moves gracefully over uneven surfaces. The goal of our project is to create a hybrid between a Strandbeest and a bicycle, allowing for maneuvering through Jansen's legs at the back and a wheel at the front.
2. Problem Statement
To address the limitation of rolling motion, our project explores more hybrid mechanisms for motion that merge the efficiency of a wheel vehicle, such as a bike, with the walking motion of a Strandbeest mechanism. We were inspired by Theo Jansen’s mechanism, the “Strandbeest Machine”, which has multiple pairs of Jansen legs and is powered by the wind. Using his concept, we wanted to replace the back wheel of a bike with 2 pairs of Jansen wheels to provide walking-based propulsion and use the front wheel for directional control. This combination aims to improve maneuverability and stability in soft terrain.
The problem statement is to design a hybrid robotic mechanism that combines the efficiency of a wheeled bicycle with the dynamic walking motion of a Strandbeest. Using Theo Jansen’s mechanism, our version of the project replaces the rear wheel of the bicycle with two pairs of Jansen-inspired legs to provide walking-based propulsion. This system will work with the front wheel providing directional control. This design achieves smooth coordinated motion, which allows the vehicle to move on soft and uneven terrain with improved stability and maneuverability. The mechanism is designed to carefully move along specific motion paths, with acceleration and force distribution to ensure effective propulsion without limiting the efficiency and structural integrity. The hybrid approach leverages multi-axis kinematics to achieve both horizontal and vertical motion. To optimize performance, we are exploring two drive options, the Geneva mechanism and a planetary gear system, both of which accommodate changing link lengths and improve the efficiency of leg movement.
3. Mechanisms
3.1 Background
To truly understand the reason why a Jansen leg is the better option than a wheel relative to soft terrain, it is helpful to compare and contrast the underlying physics behind each component of the system. First and foremost, a wheel has continuous contact with the ground all of the time. Continuous contact can be a double-edged sword – it is ideal for flat surfaces, but not so much for soft surfaces. Continuous contact relative to a soft surface means continuous resistance as well. Essentially, as the wheel rolls, it compresses the material that is in front of it, which creates a hole that the wheel must now climb out of. This propagates into what is known as the bulldozing effect, which is essentially where the energy is used to push the material out of the way instead of converting directly into forward motion.
Energy losses for a wheel in soft terrain can be decomposed into 3 stages:
Compaction Work: This is where the wheel compresses the material in front of it and rearranges the sand in front of it. The effective energy goes into deforming the surface instead of propelling the wheel forward.
Sinkage: Assuming the tire has a thin thickness (wheel can be considered narrow), having a narrow tire would produce a higher pressure. This is due to the inverse proportional relationship between Pressure and Area. Pressure is Force/Area, so having a small area leads to a higher pressure (assuming constant force is being applied). This resulting high pressure causes the wheel to sink more, and each rotation tries to get the wheel to climb out of its hole, which eats up additional energy.
Sidewall Drag: Sand is pushed to the side by the wheels, which leads to an increase in horizontal resistance. This increase in horizontal resistance leads to an increase in the amount of force needed to keep constant motion.
From this, we can conclude that if we are working with soft terrain, most of the rider’s pedaling energy is gone before any effective forward force is even created.
On the other hand, a legged mechanism (like the Jansen mechanism) acts differently. There are two phases of the Jansen mechanism: the stance phase and the swing phase. The foot only has direct contact with the ground in the stance phase. The foot rises off the ground in the swing phase and experiences zero resistance during that time period (assuming negligible air resistance). In the stance phase, the foot pushes backward, much like if a person were walking, and produces a thrust with a ground reaction force in the horizontal direction. The contact area is also larger than that of the wheel, which effectively reduces pressure and sinkage. Since there is no contact with a surface in the swing phase, there are also no external factors, such as compacting, bulldozing, or sliding friction, that would affect the system.
A wheel experiences 100% of the horizontal force at all times since it has continuous contact with the soft surface, whereas a leg mechanism only experiences it during a percentage of the cycle (usually represented as a value). If we assume to be of around 0.4 for a Jansen linkage, we can observe that just adding a swing phase, we can effectively reduce the average horizontal resistance by about 60%.
Unlike other mechanisms, the Jansen linkage configures the leg path to ensure that it is pushed forward not upward, which essentially produces mainly a horizontal force and minimal vertical motion (so no oscillations). Additionally, because the Jansen linkage fully lifts up at the time of the swing phase, there is no sliding contact with the surface i.e, no frictional resistance. The no sliding effect with the terrain mitigates the potential frictional drag and bulldozing effects.
In the stance phase, the foot only has contact with the ground. The Jansen linkage also operates on a purely rotational motion similar to the rotational motion of the wheel, which in turn makes it easier to drive with pedals.
Main takeaway: Wheels are only more efficient than the Jansen mechanism if we are working with hard ground because of the low rolling resistance. However, if we have soft terrain, high pressure due to the narrow area of the wheel causes effects such as sinkage and bulldozing which greatly increase the amount of energy loss in the system. The Jansen leg mechanism avoids this issue altogether by spreading the load over a large area and having intermittent contact with the surface by lifting between steps. It keeps the mechanical essence of the wheel which is powered by rotational motion but has the additional caveat of only touching the ground when it is necessary. This in turn makes the walking bike a real shot of winning against a wheeled bike when working with a soft terrain like mud.
The Jansen leg can maintain its ground force direction and magnitude through its linkage geometry. The foot trajectory allows the mechanism to press firmly yet gently against the terrain without continuous rolling, maintaining a non-slip interaction with the deformable surface below.
In Equation 3, the J(θ) is the Jacobian matrix that relates the crank angular velocity to the foot linear velocity. The torque equation shows that the leg can trade torque for force:
Because the Jacobian depends on the crank angle θ, there are phases where the magnitude of J(θ) is small. In these positions, even medium torque produces a large output ground force. This variable mechanical advantage allows the Jansen leg to apply strong forces at low foot velocities, making it perfect for motion over soft or uneven terrain.
3.2 Jansen Mechanism
The mechanism for the Strandbeest Bike will consist of a bike and a Jansen linkage. The Jansen Linkage is an eleven-bar 1DoF mechanism known for the simulation of organic walking [1]. The mechanism additionally contains a stationary link. [2]
Jasen uses a simple rotary input, which can be actuated using a motor or the connection of the gear of a bike. The driving input node is constrained at the origin in the Descartes coordinates. The eleven links are combinations of numbers that were generated by Theo Jasen, and these numbers have been colloquially known as the Holy Numbers.
a=38.0, b=41.5, c=39.3, d=40.1, e=55.8,
f=39.4, g=39.7, h=65.7, i=49.0, j=50.0, k=61.9, l=7.8, m=15.0
The goal of this project is to incorporate the Jasen linkage in a bike to utilize a bike’s ability to stay upright using its center of mass.
The gait is controlled by parallel motions as two symmetric legs work together, as shown in Figure 4.
3.3 Geneva Mechanism
The Geneva mechanism is a mechanical indexing system that is designed to transform continuous spinning motion into controlled, incremental movement. Essentially, as the input shaft spins continuously, the motion generated from this is transformed into individual angular steps, please shown in Figure 4. Each step of rotation is characterized by on-and-off periods of motion and dwell. The motion phase is where the drive pin interacts with the output wheel via a slot, which causes the output wheel to rotate. When the pin disengages from the system, there is no more contact between the input and output wheel, so the output wheel just remains stationary. This phenomenon results in precise incremental positioning, i.e., the output wheel progresses by a specific, repeatable amount with consistent accuracy at each increment. Due to this well-indexed stepwise motion, the Geneva mechanism is great for applications that necessitate stopping precisely in the correct spot at the end of each time period.
Equations
We can define the motion of the drive pin using two reference frames:
These two equations describe the motion of drive pin P with respect to the input and output reference frame. By equating these two equations against each other, we can calibrate the input and output velocities. From this, we can calculate the intermittent angular motion of the output disk with respect to the continuous motion of the input disk and other geometrical parameters of the mechanism.
The Geneva mechanism will be integrated into the system by attaching it to the sprocket of the bike pedal. To reiterate, the intention of integrating this mechanism is to alter the gait using mechanical means.
3.4 Planetary Gears Mechanism
Planetary Gears are a compact gear system that can change how fast the input and output gears rotate, depending on which part is fixed.
Components of Planetary Gears
Sun Gear (s): main gear in the middle
Planet Gears: gears that orbit around the Sun Gear
Carrier (c): the supporting arm or frame that holds the Planet Gears
Ring Gear (r): outer gear with internal teeth that surrounds Sun Gear and Planet Gears
How They Work
The velocities of the three main components are related through this equation:
Basically, if one knows the speed of any of the two components, you can calculate the speed of the third. Planetary gears behave like regular gears, but the supporting arm or frame that holds the Planetary Gears (the carrier) adds wiggle room in speed and control.
Transmission Ratios
Various gear ratios are derived from locking one component to another:
When the sun gear is fixed, the planetary gear provides a reduction in speed and an increase in torque at the output. We will use the equations to find the exact input and output speed of each planetary gear in the system.
4. Proposed Scope
We aim to design and fabricate a Strandbeest-inspired bicycle that combines Theo Jansen's linkage motion, including a human-powered pedaling mechanism. The final system will demonstrate a smooth, efficient walking motion, which is powered by rotational input from pedals instead of traditional wheels. The design and testing process will include motion analysis, including kinematic and dynamic. We will use Python, SolidWorks, and MATLAB to optimize the linkage geometry for stability and fluidity of motion.
The structure will be laser-cut, and the joints will be connected by 3D printed couplers. The drive train system will be changed from the bicycle/chain setup to walking linkages instead of rotating wheels.
The design process will emphasize structural integrity, gait smoothness, and energy efficiency.
- Stage 1: The modeling and CAD stage of the Strandbeest Bike is completed. The linkage dimensions and motion path will be validated using SolidWorks, and the frame will be cut and assembled to test the mechanics of the bike.
- Stage 2: We will establish a single-sided gait and then expand to design a full dual-sided Strandbeest bike that supports a load. This phase will include a pedal-driven chain mechanism to power the linkages symmetrically. Refining the geometry to improve walking efficiency.
- Stage 3: Refining and adjusting the prototype based on better materials of the finalized product, and completing the project with final additions.
5. Preliminary Design
5.1 Overall Design and Variation of Sprocket Gear Design
This is a schematic of the overall design of the bicycle with the 3 pairs of Jansen legs at the back and the wheel at the front. We also have calculated the degrees of freedom of 1 leg through the Grubler’s Equation. In addition to that, we have outlined what our 2 options may look like for the sprocket gear connecting the 3 linkage pairs. Both options will support stability and speed reduction of our overall bicycle.
5.2 CAD Design of Jansen Leg
This is our design for our Jansen Leg as of now. We will be connecting 3 pairs of Jansen Leg linkages to a rotary component that will move the legs. This will be our basis for future design additions.
Citations
[3]10 - Stair-Ascending Strandbeest
[4] Jansen Linkages