17-1 Project Proposal

1. Introduction:

Most robots use wheels because of their simplicity however, these systems struggle with off- roading and obstacles. Traditional walking robots rely on complex control systems to coordinate multiple actuators. Using a control-based system requires many sensor feedback loops, and control algorithms to manage each leg. This project proposes a walker that uses a Jansen’s eight-bar linkage to generate a walking gait. The Jansen linkage achieves a walking motion mechanically rather than computationally. Such a linkage can convert a rotational input into a complex, periodic motion without needing control systems. This allows a single motor to produce a walking motion. The project goal is to demonstrate how complex locomotion can be achieved through mechanism design, reducing the need of complex control systems, sensors, and motors.

2. Problem Statement:
Designing a robot capable of simulating a stable walking motion requires generating a complex
2D trajectory for the “foot” of each leg. Each “foot” needs to follow a path where it raises the
foot from the ground, travels forward during the forward swing phase, and returns to the ground during the return phase, where it prepares the next step. The motion is nonlinear and is difficult to achieve with a simple mechanism such as a 4-bar linkage. The challenge is to create a mechanism that is capable of generating this trajectory and repeating it.

3. Proposed Mechanism:
To generate the walking motion, the project shall utilize a Jansen eight-bar linkage mechanism.
The Jansen linkage converts a continuous rotary motion from a crank into a walking trajectory
for a foot. Multiple identical Jansen linkages will be mounted along each side of the robot
chassis to form a set of legs. The legs on each side will be connected to a shared
crankshaft so that they move in synchronized phases.

Open

The robot will also use a tank-drive configuration, similar to Build Assignment 2, where one
motor drives the left side, and the other motor drives the right side. By varying the speeds of
the motors, we will allow us to control the direction (forward and backward) and allow us to
rotate it (either in place or while traveling in a straight line).

3.1 Jansen Mechanism:

Open

Figure 2: Jansen Linkage with Link Lengths.

The walking motion of the robot is generated using a Theo Jansen linkage, a planar multi-bar mechanism capable of producing a walking gait from a single rotational input. The mechanism converts the rotation of an input crank into a complex foot trajectory consisting of a stance phase (ground contact) and swing phase the (foot lifted).

The geometry of the linkage is defined by a set of optimized link lengths often referred to as Jansen’s Holy Numbers. These link proportions produce a smooth walking trajectory when driven by a single crank.

The link lengths used in this design are:

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

These values define the relative lengths of the links shown in Figure 2, which illustrates the geometry and joint locations of the Jansen leg mechanism.

3.2 Mobility Analysis:

Using Gruebler’s equation,

For the Jansen linkage,

Thus,

so the mechanism has 1 DOF.

4. Proposed Scope of Work:

1. Analysis and design
   a. Study the Jansen linkage
   b. Perform kinematic analysis to see the foot trajectory
   c. Determine link length
   d. Analyze mobility using Grueber's equation

2. Mechanical design
   a. Create CAD models of the linkage and robot chassis
   b. Design crankshaft assemblies for both sides of the robot

3. Fabrication
   a. Manufacture linkages using laser cutting or 3D printing
   b. Assemble the chassis
   c. Connect the two motors to independently drive each side.

4. Testing
   a. Test walking stability

   b. Test turning capability
   c. Optional: measure forces on each leg (purposely overload to figure out limits)
   The final deliverable will be a functional walking robot prototype using a Jansen linkage.

5. Preliminary design ideas:

The initial design includes a robot with multiple Jansen linkage legs on each side connected where each side is connected to a crankshaft. The crankshaft is when powered by an electric motor. This connection will likely be done through gears for torque management.