Jansen's Linkage in Grasshoppper

Jansen's linkage

Leg mechanism designed by the kinetic sculptor Theo Jansen

CADLogic Form Workshop WS 2020-21 DIA, Dessau Course Advisor - Fredrik Skatar MD Ashfaq Bin Arif Mtr Nr. 4070314 08.02.2021

What is Jansen's linkage?

Jansen's linkage is a planar leg mechanism designed by the kinetic sculptor Theo Jansen to generate a smooth walking motion. Jansen has used his mechanism in a variety of kinetic sculptures which are known as Strandbeesten (Dutch for "beach beasts"). Jansen's linkage bears artistic as well as mechanical merit for its simulation of organic walking motion using a simple rotary input. These leg mechanisms have applications in mobile robotics and in gait analysis.

How does it Work?

The central 'crank' link moves in circles as it is actuated by a rotary actuator such as an electric motor. All other links and pin joints are unactuated and move because of the motion imparted by the crank. Their positions and orientations are uniquely defined by specifying the crank angle and hence the mechanism has only one degree of freedom (1-DoF).[5] The kinematics and dynamics of the Jansen mechanism have been exhaustively modeled using circle intersection method and bond graphs (Newton–Euler mechanics).[6] These models can be used to rate the actuator torque and in design of the hardware and controller for such a system.

(Source: https://www.strandbeest.com/)

Rotating joints (red)

Area of this area remains fixed Rotating point of Control

This rotating joint does not move from its point

Area of this area remains fixed

Different Parts of Jansen’s Linkage

The most amazing part about this mechanism is that there is only one control point for the whole mechanism. Also, Jenson made his models powered by wind, which is preety cool considering the source of enery to move these big sculptures comes from 100% clean energy: Wind.

A very interesting video named “STRANDBEEST EVOLUTION 2017” showing these amazing kinetic sculptures can be found here: https://www.youtube.com/watch?v=LewVEF2B _pM Cover image source: https://ifthenisnow.eu/nl/verhalen/world-artists-and-their-story-8-theo-jansen

Movement of Jansen’s Linkage

Image source: https://www.sciencedirect.com/science/article/abs/pii/S1569190X15001562

Grasshopper Script This script can be devided into three parts. Each part is shown and explained in detail in the next pages.

There is only one control point for this whole script. Which is the rotating point of control for both the legs. By rotating this point around the central axis of the first point, this mechanism can be walked.

An animated gif of the mechanism can be found here: https://drive.google.com/file/d/1MhVpNzawc7U0b7vR1gg2dzDYbCgtdseu/view?usp=sharing

Part - 1

Making the Central Parts

Part - 2

Finding the Points of Joints for the Legs

Part - 3

Connecting Lines of Each Points of Joints For the Legs

Preview

Part - 1

This is the beginning of the script. In this part the basic structure for the mechanism is created.

4

So, the mechanism starts with the points. The circle 1 is the representation of the rotating motion of the rotating handle. And then circle 3 & 4 are the two starting rotations for the legs.

And then a “POINT ON CURVE” component indicates a point on circle 1. Making this point the center, the circle 4 is made.

The next part starts based on these 4 circles.

2

1

3

Part - 2

This is the second and the most complicated part of this script.

4

From the circles 3 & 4 for each of the legs, more circles are identified based on the intersection of the circles and thus finding out the rotation points of each of the joints.

So, the intersection of the circles 3 & 4 are found out with the component “CURVE CURVE” and two points of intersection are found. Then with a “LIST ITEM” component each of these intersection points are separated to make two new circles.

And then the rest of the construction is based on the same principle.

3

Part - 3

This is the final part of the script. The leg parts are constructed here.

The are 10 part for each of the leg of this component.

From the intersection points figured out in the second part, lines are constructed to find out each part of the legs.

Finally, when both the legs are constructed, the mechanism is complete. By rotating the point on the first circle, the whole mechanism can be moved.

Ideas for Model Different types of models can be considered to understand this leg system mechanism>Some models can be built as partial, like just one part of the system or just one leg. >Or the whole system in a planar configuration. > Also a full walkable model can be built with foue legs.

Additionally, it is interesting to point out that in the stransbeest website they are selling a model kit with which anyone can build a mini stransbeest.

This is a partial model made with PVC pipes, mainly to study and understand the mechanism behind the idea.

This is a study model. Only two planar legs are shown here. This model is done with popsicle sticks and joints are made with pins. A cardboard sheet is used as base.

This full walkable model is made with DC motors and all the joints and leg parts are made with 3D printing pen.

This model is made of plastic, includes illustrated and written instructions, and requires no special tools.

Thank you