Mimicking the motion of a Coconut Crab using 1-degree of freedom planar mechanisms

Team Members: Cecilia Corral, Haoran Xie, Pradeep Radhakrishnan and Sadhan Sathyaseelan

Introduction

Our goal is to mimic the motion of a coconut crab using one-degree of freedom planar mechanisms. An example of a coconut crab is shown in the video below. 

As you may notice in the video, there are two pairs of legs on either side of the crab body in addition to a pair of claws on the front and a pair of small legs on the rear side. The two pairs on either side are the main source of motion. The front claws and the rear legs serve as support apart from the obvious predatory function of the front claws. Though the crab can be categorized into a multi-degree of freedom system, we felt that it is possible to divide the motion into two categories - planar and lateral movements - by repeated analysis of the video (see above). Therefore, we are investigating through this project, the ability of 1-dof planar mechanism to mimic the planar motion of each leg in the coconut crab. If this attempt is successful, our goal of proving that simple mechanisms can predict complex motions will be achieved.

Tasks

In order to achieve our goal, we had decided to divide our work into several tasks and those are listed below. 

Mapping the Trajectory

The trajectory of each joint was mapped for every step made by the crab from the video. An example image with the joints on each leg marked is shown below. 

The joints are connected by links. At the time of mapping the trajectory, we did not assign any type for these joints. To make it easier for us to map the trajectory, we developed a MS -EXCEL VBA program to enable us to easily mark these joints and extract (x,y) coordinates of these points. A total of 5 points were extracted. The MS EXCEL VBA program and the values can be found in the attachment below.  [Book1.xlsm]

Synthesis

The trajectory mapped 5 points, which leads to 5 different link positions. In order to apply the Graphical three-position synthesis, we are considering the first , third and the final positions as shown in the figure below for the rear leg. 

It should be pointed out that the graphical three position synthesis is usually applicable only for one link in a mechanism consisting of revolute joints. But since our requirement is to have one mechanism replicating the motion of three links, we decided to independently carry out three-position synthesis for these links and merge them on to the same mechanism. The links are assigned measurements 2.5in, 4in and 3in for the top, middle and bottom links respectively. The three position synthesis for the rear leg is shown in the figure below (shown along with construction lines). The corresponding AutoCad file is also attached (?rear-new-differentlengths.dwg). 
The links are denoted by the lines displayed in red and the dark circles indicate the ground locations. Autocad Force Effect Motion software available as an application on iPad is used to simulate the mechanism. The photo attached below displays how the mechanism for the rear leg looks within that application. 

The links BC, CE and EG are the required links for the rear leg and A, F and D are the grounded points. The trajectory mapped by the joints B,C, D and E are shown in blue. The arrows along the trajectory indicate the respective joints' velocity and acceleration. Similarly, the position synthesis of the front leg can be found below (shown along with construction lines) and the corresponding AutoCad file here ( front-differentlengths-twopos.dwg ). 

Based on a careful analysis of the front leg in the video, we felt that the links attached to the leg do not make complex motion and decided to adopt the first and last position for synthesis. This simplification led to us using the Graphical Two-position Synthesis technique. 

As you may note, the trajectories mapped by the joints do not map the actual one (as shown in the rear-leg screenshot of AutoDesk Force Effect Motion). At the same time, the required motion of links is also not achieved since the three-position synthesis has led to a mechanism with toggle positions after 60deg rotation. Similar effects were noted for the front leg mechanism with revolute joints. Also the legs do not lift and return to their original position as can be in the original crab video.This made us realize the limitations of graphical synthesis techniques for complex motions such as replicating the movement of a coconut crab and the need to improve the mechanism. 

Improvements to Synthesized mechanisms

The planar mechanisms generated in the previous task led to inaccurate replication of motion and needed improvement. The improvement may also require including additional joint types such as Prismatic and pin-in-slot type (R-P) joints. We had to employ a trial-and-error method to synthesize the required mechanisms since there are no specific guidelines for synthesis available in literature. The improved mechanism for the rear-leg is shown below after several iterations. 

You may notice from the video that there are revolute joints, prismatic joint (joint K) and the pin-in-slot joint between joints D and B. The improved mechanism also involves a 360-deg input crank rotation and a lift before returning to its original position. Also, DEH is one link since we realized that there is no significant relative movement between the top (DE) and the middle link (EH) in the rear leg. Also, the bottom link is HI, which again is connected by means of welded joints to the sliding joint K. 

Similarly, the front leg was synthesized as shown in the video below. 

DC,DB and BA are the three links that constitute the front leg, but due to negligible relative movements, they have been designed as a single link. 

Though the trajectories are still not mapped accurately, we feel that this is a good starting point for building the prototype for testing. We are hopeful of employing optimization techniques to further improve the mechanisms. 

The front claws and the rear-leg for support were also synthesized and can be viewed in the videos attached. Front-Claw.mp4 ; Rear-Support Leg.mp4

The front claw mechanism is designed as a support and does not include an input crank. The rear support leg is comprised of a slider-crank mechanism. 

Attachments: 

Autodesk Force Effect Motion files: Rear_Leg_ForceEffectMotion.afem; Front_ForceEffectMotion.afem ; Front_Claw_ForceEffectMotion.afe ; RearSmallLeg_ForceEffectMotion.afem

Prototyping

The front and rear legs were only considered for prototyping. For prototyping, we decided to build the mechanism in Pro/E to detect potential assembly issues. The Pro/E simulation that we decided to adopt for final prototyping is available here. Pro/E Model 1.mpg ; Pro/E Complete Assembly.mpg

The files used for the assembly can be found here - Assembly STEP File.stp

The various links were cut on Acrylic sheets using Laser Cutting process. The following pictures are reflective of the stages in prototyping and assembly. 
(The figure shows the first iteration with revolute joints below and the new mechanisms above)

(Actual Prototype - constructed using Foam Board and Acrylic sheet for links)

(Top view of the transmission system. Belt drives were used from a single input motor to operate all four legs. The front claws and the rear support legs were not incorporated into the current prototype but will be done at a later stage.)

(Close-up view of the transmission system)

Issues

Though our prototype was built and was light-weight, the prototype did not function as we had hoped to (can be seen in this video : Prototype Video.mov 

We think some of the issues are due to the following reasons:
1. Use of foam board - this makes aligning shafts difficult since perfect alignment is required for belt drives. In addition, the sliding joint for the rear leg were not moving as we desired due to the friction induced by the foam board surface. 
2. Absence of Flat Legs - our leg design had pointed legs, which made transfer of weight to the links and joints difficult. This added additional resistance on the sliding joints and pin-in-slot type joints, thereby leading to stalling of the mechanism. This led to slippage of belts from the sprockets. 

Future Work

Though our model had limitations, our 1-dof planar mechanisms to mimic the planar motion of the coconut crab shows promise. Since our current prototype had several issues, we propose to the following so that we are able to produce a better mechanism and prototype.

Synthesis:

1. Adopt multi-objective optimization strategies for optimizing links and ground locations to yield more accurate trajectory and motion match

Prototype:

1. Develop better legs

2. Study the effects of dynamics

3. Avoid the use of Foam and possibly make use of Acrylic or any other material to ensure limited assembly variations and alignment issues

Team at Work: 

(Photographer: Pradeep)