16.2 Kinematic Analysis
Overview
Our objective is to create a Morse Code encoder machine that can utilize distinct motion profiles to stamp a dot, a dash, and a space onto a piece of paper. To accomplish this, we evaluate the gait profiles of two candidate walking mechanisms: the Klann and the 8-Bar.
Both mechanisms take a full rotational crank input and produce a smooth gait profile featuring a flat segment along the lower portion of their path. This flat region can be used to inscribe Morse code symbols by adjusting its length and orientation. While other gait mechanisms were briefly considered, these two were ultimately selected for their use of three ground joints – providing multiple joint to reposition to alter the motion profile – and their ease of implementation.
The two motion profiles are shown below:
Based on these motion profiles, the goal of this analysis is to identify specific configurations that can reliably produce distinct “dot” and “dash” characters, i.e. short and long flat segments, while maintaining minimal variation in height and lateral displacement for symbol printing.
Positional Analysis
To evaluate the motion profiles of the Klann and 8-bar mechanisms, we conducted a vector loop positional analysis. Initial diagrams were sketched by hand, then calculations were translated into Python scripts for flexible simulation of link lengths and joint positions.
Preliminary testing and literature review showed that adjusting the ground joint positions, in relation to each other, was the most effective and practical way to modify the motion profile. Unlike changing link lengths – which would require complex slotted mechanisms – this approach is easier to implement. Once again, this was a key reason for selecting the Klann and 8-Bar systems, as both offer three manipulable ground joints.
Klann Mechanism
The Klann mechanism is a 6-bar linkage with 7 joints – three grounded and one ternary. It can be decomposed into two 4-bar vector loops, highlighted in the diagram, along with the adjustable ground positions.
Vector Analysis
The vector loops were solved using basic kinematic equations while preserving vector directionality. Joint positions B and C were computed first to solve the second loop, forming the basis of our code for analyzing its motion profile.
Vector Loop 1:
Dynamic Link:
Vector Loop 2:
End-Effector Trajectory:
Preliminary Prototype Configuration
Preliminary analysis showed that varying link lengths was not only impractical but often resulted in “broken” configurations that couldn’t complete full crank rotations (Non-Grashof linkage). Therefore, to efficiently explore gait patterns, link lengths were kept constant. Note however, for added design flexibility, links 3 and 6 were divided into two pieces with adjustable angles, though they will function as continuous links in the final design.
After manual testing, the following parameters were selected, resulting in the motion profile shown below:
Link | Length (cm) |
|---|---|
LA | 7.0 |
LC | 6.3 |
L2 | 3.0 |
L3 | 6.6 |
L3b | 5.8 |
L4 | 3.6 |
L5 | 6.0 |
L6a | 10.0 |
L6 | 20.0 |
8-bar Mechanism
The 8-bar mechanism is an 8-bar linkage with 7 joints – three grounded and on ternary. It can be decomposed into three distinct 4-bar vector loops, highlighter in the diagram, along with the adjustable ground positions.
Vector Analysis
The vector loops were once again solved using basic kinematic equations while preserving vector directionality. This time around however, three vector loops were needed, requiring additional calculations.
Vector Loop 1:
Vector Loop 2:
Dynamic Link:
Vector Loop 3:
End-Effector Trajectory:
Preliminary Configuration
Once again, preliminary analysis showed that changing link lengths often resulted in “broken” configurations. Therefore, link lengths were kept constant. Similarly, link 7 was temporarily divided into two pieces with adjustable angles, for added design flexibility.
After manual testing, the following parameters were selected, resulting in the motion profile shown below:
Link | Length (cm) |
|---|---|
LA | 7.5 |
LC | 5.0 |
L2 | 2.0 |
L3 | 7.0 |
L4 | 4.5 |
L5 | 5.5 |
L6 | 4.0 |
L7a | 7.0 |
L7b | 3.0 |
L8 | 5.5 |