Wing Mechanisms

Repurposing Jansen’s Leg Mechanism:

Innovative mechanical flyers were designed by student teams in my Kinematic Synthesis class based on a repurposed version of Jansen’s leg mechanism. The artist Theo Jansen has inspired many of my students with his dramatic assemblies of leg mechanisms to form his Strandbeest wandering on a beach under the power of a sea breeze. 

A generalization of Jansen’s leg has the hip and knee joints driven by separate four-bar function generators to provide a wide variety of foot trajectories. This generalized version of Jansen’s linkage can be adapted to form a wing mechanism that has a desired wing-tip trajectory. 

This video shows the Geogebra model of a wing mechanism based on Jansen’s linkage, and three digital prototypes of mechanical flyers obtained by my students using this mechanism.

21st Century Kinematics: NSF Workshop

I am pleased to provide the presentations from the 2012 National Science Foundation Workshop on 21st Century Kinematics. These presentations provide insight to the challenges and opportunities for research in mechanical systems and robotics.

The NSF Workshop on 21st Century Kinematics at the 2012 ASME IDETC Conference in Chicago, IL on August 11-12, 2012 consisted of a series of presentations and a book of supporting material prepared by the workshop contributors.

The book is available at 21st Century Kinematics–The 2012 NSF Workshop.

And here are the presentations given at the workshop.

  1. Computer-Aided Invention of Mechanisms and Robots. J. Michael McCarthy, Professor, University of California, Irvine.
  2. Mechanism Synthesis for Modeling Human Movement Vincenzo Parenti-Castelli, Professor, University of Bologna.
  3. Algebraic Geometry and Kinematic Synthesis. Manfred Husty, Professor, University of Innsbruck.
  4. Kinematic Synthesis of Compliant Mechanisms. Larry Howell, Professor, Brigham Young University.
  5. Kinematics and Numerical Algebraic Geometry. Charles Wampler, Technical Fellow, General Motors Research and Development.
  6. Kinematic Analysis of Cable Robotic Systems. Vijay Kumar, Professor, University of Pennsylvania.
  7. Protein Kinematics. Kazem Kazerounian, Professor, University of Connecticut.
  8. Development of Fast Pick and Place Robots. Jorge Angeles, Professor, McGill University.
  9. Kinestatic Analysis of Mechanisms with Compliant Elements. Carl Crane, Professor, University of Florida.

It seems time to consider another similar workshop for 2022.

The Bored Robot: Controlling Two Drive Motors for a Walking Machine

Brandon Tsuge describes how to assemble the controller for two motors to drive the right and left sides of a walking machine using an RC transmitter and controller. See The Bored Robot: Using a DC Brushed Motor with a Rotary Encoder.

How to Fix SW Motion Analysis Error: Too Many Redundant Constraints

Kevin Chen,  J. Michael McCarthy,  Shaun Bentley

The design and assembly of our four-legged mechanical walkers can yield single degree-of-freedom systems with so many redundant mates that it stalls SolidWorks’ Motion Analysis.  For example, the walker shown in Figure 1 had 782 redundant mates.   The procedure outlined below reduced the number of redundant mates to 114, and Motion Analysis executed efficiently.

Four-legged Walker Assembly
Figure 1.  A four-legged mechanical walker consisting of a body, drive train, and four-leg mechanisms.

Our walker consists of a body, drive train, and four legs.  The legs mechanisms are identical but assembled as front-to-back mirror images.  The component parts of this walker mates were assembled using mates to align and coordinate various subassemblies, resulting in a large number of redundant mates.

In order to reduce the number of redundant mates, we dissolve the subassemblies, combine rigid elements, and mate new subassemblies as follows.

Step 1

Dissolve all of the subassemblies in the walker. To do this, hover over each assembly and select the menu item Dissolve Assembly. See Figure 1.

New Sub Assemblies
Figure 2.  Selected parts for new subassembly.

Step 2

Form new subassemblies for each leg, the drive train, and the body. See Figure 2. To do this, first, hover over the part, press “tab” to hide the part in order to identify it easily; and then, select all of the hidden parts, and right-click to open menu and select Form New Subassembly.

Form New Assemblies
Figure 3.  Within each new subassembly form subassemblies of parts that do not move relative to each other.

Step 3

Within each new subassembly combine parts that do not move relative to each other.  See Figure 3. The tree structure should consist of separate assemblies of rigid elements with the remaining mates between the assemblies. See Figure 4. 

Rigid Elements
 Figure 4.  The assembly should consist of subassemblies that move as rigid elements relative to each other.

Step 4

 Repeat Step 3 for all of the new subassemblies.  The result is shown in Figure 5.

Rigid subassemblies
 Figure 5.  The subassemblies that define the mechanical walker.  Notice that the tree structure consists of subassemblies and no individual parts.

Step 5

Delete the mates in the main assembly.  Introduce the mates required for movement using hinge mates, rather than coincident or concentric mates, where possible.

Step 6

Make the subassemblies at the top-level flexible.  Right-click on the assembly and select the flexible assembly icon  pastedGraphic.png.

The result of this procedure is a system with 114 redundant mates that Motion Analysis can process effectively.  The result is that animation shown below.

Six-Legged Mechanical Walkers: Spring 2020 Highlights

The leg mechanisms of these six-legged walkers use two coordinated function generators to drive the hip and knee joints to achieve the desired foot trajectory. This differs from Jansen’s leg mechanism in the following ways: (i) separate cranks can be used to drive the hip and knee joints, rather than the same crank driving both joints; (ii) the drive of the hip joint need not be connected at the knee but can connect any where on the upper leg; and (iii) a true parallelogram is used to connect the drive around the hip down to the knee, whereas Jansen’s connection has one side slightly larger for both pairs (39.3, and 39.4 for one pair of sides, and 40.1 and 36.7 for the other pair). So these leg mechanisms can be viewed as generalizations of Jansen’s design.

Stable gait for these walkers can be achieved by coordinating three legs at a time to form a tripod gait.  Please see this video showing walkers designed by my students to be a crocodile, rhinoceros, bug, legged container and the Star Wars All-Terrain Tactical Enforcer, known as AT-TE. These assemblies of six 10-bar linkages connected by a gear train of as many as 18 gears posed a challenge to SolidWorks motion analysis for my students. We will get better at this.

Prototype Four-Legged Mechanical Walker

Kevin Chen and Arwa Tizani designed this four-legged mechanical walker using Curvature theory to identify a flat-sided coupler curve of a four-bar linkage. This curve was positioned to be the foot trajectory of the leg mechanism using a skew-pantograph.

Kevin collected the parts and assembled the walker. Here are his photos and video of its performance:

Four-Legged Mechanical Walkers: Spring 2020 Highlights

The design of these four-legged walkers relies on Curvature theory to find a flat-sided coupler curve of a four-bar linkage to be used for the foot trajectory. This coupler curve is repositioned using a skew pantograph. The result is a six-bar leg mechanism.

Stable gait for these walkers can be achieved by adding side-to-side foot extensions to broaden the support polygon during walking.

Please see this video showing walkers designed by my students to be a rabbit, two dogs, a bear, a rhinoceros, a dinosaur, and a centaur, as well as a legged platform, a legged syringe and the Star Wars All-Terrain Attack Transport, known as AT-AT.

The Design of Mechanical Walkers: Spring 2020 Student Projects

While isolated to slow infections of the Coronavirus, over 60 UCI students learned how to apply the principles of Curvature Theory and Finite-Position Synthesis to the design leg mechanisms for mechanical walkers.

Their first team project was a four-legged walker that used the coupler curve of a four-bar linkage positioned using a skew-pantograph as the foot trajectory. Here are videos that show animations of their walkers

This is the first video:

And this is the second:

The final team project used finite-position synthesis to design function generators to drive the hip and knee joints and guide the foot trajectory. This mechanism is a generalization of the Jansen leg mechanism. Teams of three students designed the leg mechanism, the drive system and assembled them into a six-legged walker. Here are the videos of these walkers.

This is the first video:

And this is the second video:

The variety of these walkers show the versatility of the kinematic synthesis procedures, as well as the creativity of the students. It was a pleasure working with the students on these projects even with the challenges of remote instruction.

Fall 2019 Mechanical Walker Prototypes

I was pleased to have an enthusiastic group of graduate students work with me on the design of four-legged walkers as the final project for MAE 245 Kinematic Synthesis. Each of the teams designed a four-bar linkage using Curvature Theory to obtain a coupler curve with a flat portion that could be used as the foot trajectories for the legs of the walker.

Then, they placed the coupler curve in position to form the feet of a walker by using a skew pantograph for the front legs and rectilinear six-bar linkages for the rear legs. I required this particular choice of the type of legs, simply because I was not sure which would work better.

This video shows the operation of their design prototypes. They all work as designed, though we have more work to do on their fabrication in order to improve performance.

Four-legged Mechanical Walkers: Teams 2, 4 and 5

Here are videos of the designs for the four legged mechanical walkers obtained by Teams 2, 4 an 5. This is the final project in my Fall 2019 Kinematic Synthesis course.

Team 2

Mechanical Walker Team 2

Team 4

Mechanical Walker Team 4

Team 5

Mechanical Walker Team 5