Project Strandbeest Final Report

Strandbeest

Final Report

Group Members:

Michael Ache

Allen Joseph

Sean Treiber

Uduak Udongwo

EML 4024C

Spring 2015

April 29, 2015

Introduction

The strandbeest is a self propelling device that is driven by wind power in theory. That is where

the inspiration for our model originates. Our model began with a simplified model of a strandbeest and

grew more complex as different characteristics were seen to be lacking in our initial model. We improved

on these points and our initial model grew. This allowed our model to improve greatly and transform into

our final model assembly. The model that was built in SolidWorks is a model that is actually a feasible

concept to achieve.

The analysis examined the static forces acting on the model and the kinematics involved within

the model. The analysis focused on the force acting on the housing and the kinematics of the leg

assembly. These results were realistic to that of an actual strandbeest model and proves that our model is

valid. The modeling, analysis, and assembly of this project are described in detail throughout this paper.

Mechanical Design

I. Crank Housing Assembly

Crank We started off with building a crank sub-assembly. A sketch was created on the right plane. It is just a simple circle sketch with a diameter of 0.75”.

Figure 1: Right Plane Sketch for Crank

Another sketch was created on the front plane. This gave the profile that the circular sketch above was to follow for the spline.

Figure 2: Front Plane Sketch for Profile of Spline

The two sketches above are used in a spline command and the crank is now complete.

Figure 3: Completed Spline. Single Crank.

Crank Case/Motor Housing The motor housing is created. A sketch is created on the front plane and is then extruded. The plate after extrusion is complete and a cut extrude is created in the center of the face. The cut extrude is the connection point for the crank to rotate within the motor housing.

Figure 4: Motor Housing after initial extrude

On the opposite side of the housing an extrude is performed in the center of that face. Two Filets are performed in the outer side of the extrusion. An extrusion cut and chamfer are used on the inner side of the extrusion created above. The female housing is now completed.

Figure 5: Female Housing Complete

An extrude and a chamfer are used in the female hole of the housing. This created the male connection rod as seen in the figure to the right. The male housing has the rod now placed within the female housing. The male housing is now complete.

Figure 6: Male Housing Complete

Support Member Middle We start by extruding on the front plane. Three extrude cuts are performed in order to create the contact points for the rods.

Figure 7: Support Member Beam

An extrude is then performed and the results merged in order to create a single piece for the motors to rest and beams to be supported. An extrude cut is performed from the top plane on the extruded portion in order to refine the edges.

Figure 8: Support Member platform created

Support Member End The two support member ends used were modified middle members. an extrude cut was used for one end of the member. The comparison can be seen in the figures to the right.

Figure 9: Comparison of End Member vs. Middle Member

Housing The housing was created using a 3D sketch and weldments. The sketch was then converted into structural members. The housing was created.

Figure 10: Final Housing

Housing Joint To create the housing joint, an extrude is created on the front plane. Two cut extrudes are then used on the appropriate faces. The extrude cut that is on the right face is then finished with a chamfer. The housing joint is complete. It can now connect the housing directly to the male end of the motor housing.

Figure 11: Housing Joint

II. Leg Structure

Straight Links: The majority of the leg members were created using a boss extrude from a straight shot with added rivet holes. The lengths of the members dictate the kinematic relations and motion of the overall leg assembly, so the distance between the connecting rivet holes is the most important parameter with respect to motion. Each of the following Links were created in a configuration derived from one to save time in assembling These lengths correspond to Theo Jensen’s calculations.

Link “C” Length between rivet holes was 39.3 inches Thickness was 1 inch and the rivet holes were made to be 0.75 inches in diameter.

Figure 12: Link “C”

Link “F” Length between rivet holes was 39.4 inches Thickness was 2 inches and the rivet holes were made to be 0.75 inches in diameter.

Figure 13: Link “F”

Link “J” Length between rivet holes was 50 inches Thickness was 2 inches and tolerances were extrude cut to prevent interference and maintain symmetry in the overall leg assembly. The hole with the tolerance cut out was given a diameter of 1.32 inches to allow for the frame to properly run through.

Figure 14: Link “J”

Link “K” Length between rivet holes was 61.9 inches Thickness was 2 inches established by the boss extrude. The holes were made to fit the rivets so they are 0.75 inches in diameter. Tolerances were added but extrude cutting rectangles down across the front face of “K” This was done to prevent interference and maintain symmetry in three dimensions.

Figure 15: Link “K”

Upper Ternary Link The upper triangular piece was constructed so the the lengths between the rivet hole which are located at the three corners of the ternary link are spaced at 41.5 inches, 55.8 inches, and 40.1 inches respectively. This was done using three straight shots and the power trim tool. This sketch was followed by a boss extrude. The rivet holes were done in the outer corners to fit the rivets ( 0.75 inch diameter, but the center hole was made larger, 1.32 inches in diameter to fit the motor base platform.

Figure 16: Upper Ternary Link

Lower Ternary Link The lower triangular piece was created using three straight shots of lengths 36.7 inches 65.7 inches and 49 inches respectively. The rivet holes were created in the corners of the triangle, each with a 0.75 inch diameter. A boss extrude and fillets finish the component. The bottom corner features two holes, this was done to prevent rotation in the foot during motion of the strandbeest.

Figure 17: Lower Ternary Link

Rivet The rivet was created by revolving a 2D sketch about a central vertical axis. The inner diameter of the revolved sketch was set to match the diameter of the rivet holes extruded in the links. 2 configurations were made in order to accommodate variable lengths required depending on the joint. If a joint required 4 links to be constraint to each other, as opposed to 2 links, the length must be longer. The two lengths were 4 inches and 6 inches, which was dictated by the thicknesses of the links.

Figure 18: Rivet

Foot The foot was created by first revolving a 2d sketch and followed with a vertical boss extrude and the rivet holes were extrude cut for the boss extrude. Two rivets were used to ensure no rotation in the foot. when used on the end of the lower ternary link.

Figure 19: Foot

Assembly

I. Housing Sub-assembly

Crank Sub-Assembly

We start by assembling the crank assembly. One end of the

crank is mated concentrically and coincident with the

appropriate hole of the motor housing. The other end of the

crank is attached to an end of another crank component. This

component is constrained perpendicular and coincident to the

one next to it

Figure 20: Single Crank

constraints

This operation is completed for all four crank components, the

completed sub-assembly product can be seen to the right.

Figure 21: Completed

Single Crank Assembly

Full Crank Assembly

The male motor housing is mated to the female motor housing.

The steps for the Crank Sub-Assembly are then repeated here.

Figure 22: Motor Housing

Mates

The two crank assemblies completed to create the Full Crank

Assembly shown to the right.

Figure 23: Full Crank

Assembly

Middle Member Connections

The Middle Support Member is mated to the Center Motor

Housings and the end rails of the housing. This member will

reduce flex in the middle section of the assembly.

Figure 24: Middle Support

Member Mates

End Member Connections

The End Member Support is mated to the motor housing at the

end of the assembly and the rails. This member reduces flex and

supports the motor.

Figure 25: End Support

Member Mates

Housing Joint Connections

The housing joint is mated concentrically and concentrically to

the appropriate component. The final mates can be seen in the

figure to the right.

Figure 26: Housing Joint to

Motor Housing (Male)

Final Housing Sub Assembly

The Final Housing Sub Assembly is now complete and can be seen in the Figure Below.

Figure 27. Final Housing Sub Assembly (Isometric View)

II. Legs Sub-assembly

Link Assembly

The Lower Ternary Link was mated coincidentally with

the Links “C”, “K” and “F”. The corresponding rivet

holes were mated concentrically to allow to the rivet to

enter. The Upper Ternary was mated in a similar fashion

to the Links “J”, “F” and “C” utilizing concentric mates

at the rivet holes and coincident mates on touching

surfaces. This link assembly forms the majority of the

Single Leg assembly.

Figure 28: Mates for the Lower

Ternary Link and adjoining Links

Figure 29: Mates for the Upper

Ternary Link and adjoining Link

Foot Mates

The foot was mated coincidentally with the inner face of

both of the lower ternary links and simultaneously

concentrically to the two rivet holes extrude cut into the

bottom corner of the lower ternary link.

Figure 30: Mates for the foot in

the leg sub assembly

Rivet Mates

The Rivets were concentrically mated to each of the rivet

holes. The longer was used to bind the joints that required

4 links to be constrained. The inner surface head of the

rivet was coincidentally mated to the outer surface of the

outer link at each of the joint intersections.

Figure 31: Rivet Mates

2- Leg Assembly Mates

In order to simplify the final assembly model the single

leg sub assembly was taken into a new assembly and

duplicated. This was done by mating the crank shaft holes

in the 2 “K” Links and 1 “J” Link. Also the Right , Top

and Front Planes and for each of the single legs were

mated coincidentally to the Right, Top and Front Planes

of the Assembly.

Figure 32: Leg Assembly Mates

Figure 33: Isometric View of 2-Leg Assembly.

Figure 34: Front View of 2-Leg Assembly.

III. Final Assembly

Leg Sub-Assembly to Housing Sub-Assembly

The Leg Sub-Assembly is attached to the Housing Sub-Assembly

through a series of mates. The mates used were three concentric,

and one distance mate. The first concentric can be seen in the

figure to the right. The same concentric mate is used on the

opposite side of the leg and housing assembly to attach the leg sub-

assembly to the housing sub-assembly. Figure 35: Mate of Leg to

Housing

Another concentric is used to connect the Leg Sub-Assembly to

the Crank. This position to connect to was chosen because when

rotating this part of the leg assembly, the legs will move in a

walking manner.

Figure 36: Connection of

Leg Sub-Assembly to

Crank

The Distance mate is then used to set the leg assembly in the

center of the crank. This distance varies for each leg assembly.

Figure 37: Distance Mate

Final Assembly Complete

Figure 38: Final Completed Assembly (Isometric View)

Figure 39: Final Assembly (Top View)

Figure 40: Final Assembly (Right View)

Strandbeest Exploded View

Figure 41: Front View of The Exploded View for the Final Assembly

Figure 42: Isometric View of The Exploded View for the Final Assembly

Figure 43: Isometric view of exploded view of Leg subassembly

Figure 44: Front view of exploded view of Leg subassembly

Mechanism Model Analysis

The entire mechanism of the Strandbeest was constructed out of a selection of plastic material,

including the hardware and the joints. The major components, such as the crank, housing motors, leg

links, and the 3D housing was made out of Nylon, PP Copolymer, Delrin, and PVC Rigid plastics

respectively. Nylon is well known for its high fatigue strength and are used for latches, gears,

and other moving parts. The advantage of the leg links’ material is that Delrin, or Acetal, holds

great impact resistance, dimensional stability, and surface hardness.

The total weight of the strandbeest, not including the top flat plate, was computed as 2077.55 lbs.

The density associated with this weight was approximately 0.0362 1bs/cubic in. The mechanism is

heavier than expected mainly because of the eight pairs of tall legs that were driven by the crankshaft.

The overall height of the strandbeest was along the y-axis and the ground was parallel to the x-z plane.

Due to the construction of the strandbeest with a multitude of ternary links, the moment of inertia taken at

the output both taken at the center of mass and the output coordinate system yielded the largest value in

the z-z position respectively.

Plastic materials unfortunately have a lower modulus of elasticity than metals and other

heavier/more dense materials. Although manufacturing a strandbeest out of metal or wood might cost

more, it will severely enhance the longevity of the product.

Table 1: Mass Properties of Individual Components

Sub-Assembly Name Mass (lbs) Volume

(cubic in.)

Density

(1bs/cubic in.)

Material

Housing Crank (x10) 1.0422 20.6056 0.0506 Nylon 6/10

Housing Male

(x3)

10.4189 324.0395 0.0322 PP

Copolymer

Housing Female

1

10.3279 321.2072 0.0322 PP

Copolymer

3D Housing

Model

28.5223 607.3027 0.047 PVC Rigid

Housing Joint 1 2.1269 44.9402 0.0473 PEEK

Housing Joint 2 2.1269 44.9402 0.0473 PEEK

Support 1 37.6678 739.4618 0.0509 Delrin 2700

NC010

Support 2.0 33.0336 648.4883 0.0509 Delrin 2700

NC010

Support 2.1 33.0336 648.4883 0.0509 Delrin 2700

NC010

Leg Assembly

(8x)

All parts for legz

1

15.0667 295.7775 0.0509 Delrin 2700

NC010

All parts for legz

2

12.4528 244.4633 0.0509 Delrin 2700

NC010

All parts for legz

5

12.6722 248.77 0.0509 Delrin 2700

NC010

Lower Ternary

Link (x2)

22.7092 445.8072 0.0509 Delrin 2700

NC010

Upper Ternary

Link (x2)

20.6235 404.8626 0.0509 Delrin 2700

NC010

All parts for legz

(x2)

18.1643 356.585 0.0509 Delrin 2700

NC010

Foot 1 3.4225 99.7196 0.0343 Polyethylene

Cross-Linked

Rivet (x5) 0.1256 3.2793 0.0383 PPE

Rivet Type2 0.1594 4.1629 0.0383 PPE

Table 2: Mass Properties of Final and Sub-assemblies

Mass properties

Configuration: Default

Coordinate system: -- default --

Housing Sub-Assembly

Mass = 186.4333 pounds

Volume = 4191.7922 cubic inches

Surface area = 16052.3205 square inches

Center of mass: ( inches )

X = -74.4812

Y = -254.7264

Z = 5.9766

Principal axes of inertia and principal moments of inertia: ( pounds * square inches )

Taken at the center of mass.

Ix = (1.0000, 0.0002, 0.0013) Px = 77123.5531

Iy = (0.0013, 0.0046, -1.0000) Py = 678831.4988

Iz = (-0.0002, 1.0000, 0.0046) Pz = 713789.9714

Moments of inertia: ( pounds * square inches )

Taken at the center of mass and aligned with the output coordinate system.

Lxx = 77124.6629 Lxy = 98.4548 Lxz = 811.5806

Lyx = 98.4548 Lyy = Lyz = -162.0011

713789.2042

Lzx = 811.5806 Lzy = -162.0011 Lzz = 678831.1561


Taken at the output coordinate system.

Ixx = 12180608.2821 Ixy =

3537171.2560

Ixz = -82178.3216

Iyx = 3537171.2560 Iyy =

1754677.3843

Iyz = -283988.2938

Izx = -82178.3216 Izy = -

283988.2938

Izz = 13809884.1929

Legs Sub-Assembly





X = -74.4200

Y = -278.5196

Z = 6.1177



Ix = (0.2439, 0.0097, 0.9698) Px = 5499858.0245

Iy = (0.9698, 0.0012, -0.2439) Py = 6527756.7510

Iz = (-0.0036, 1.0000, -0.0091) Pz = 7946189.5211



Lxx = 6466645.7657 Lxy = 7481.3078 Lxz = 243042.2048

Lyx = 7481.3078 Lyy =

7945958.7374

Lyz = 22500.7742

Lzx = 243042.2048 Lzy =

22500.7742

Lzz = 5561199.7935



Ixx = 155578162.6479 Ixy =

39830627.3573

Ixz = -631680.2347

Iyx = 39830627.3573 Iyy =

18658546.8348

Iyz = -3251180.5915

Izx = -631680.2347 Izy = -

3251180.5915

Izz = 165241490.7938

Final Assembly





X = -74.42

Y = -276.68

Z = 6.11



Ix = (0.43, 0.01, 0.90) Px = 6099856.96

Iy = (0.91, -0.00, -0.43) Py = 6733422.18

Iz = (-0.00, 1.00, -0.01) Pz = 8537286.32



Lxx = 6618786.22 Lxy = 7361.71 Lxz = 243855.08

Lyx = 7361.71 Lyy =

8537067.64

Lyz = 21825.99

Lzx = 243855.08 Lzy = 21825.99 Lzz = 6214711.60



Ixx = 165731328.94 Ixy =

42787143.95

Ixz = -700379.06

Iyx = 42787143.95 Iyy =

20122131.54

Iyz = -3488391.45

Izx = -700379.06 Izy = -

3488391.45

Izz = 176757363.39

Mechanism Static Analysis

To effectively output a static analysis of the strandbeest when a distributed load is

applied, a plate with inserted and fixed onto the top perimeter of the pipe housing. In order to

simplify the failure analysis, only the housing was evaluated with a force applied. The entire

strandbeest contained an abundance of mates of joints. As a result of this, meshing the entire

strandbeest model for static analysis was not ideal because of the potential minor interferences

within the leg assembly. The housing sub-assembly is vital because it holds the whole

strandbeest and the connecting crankshaft together, therefore assumptions can be used on the

performance of the legs when a downward force is applied to the top plate.

Before running the simulation, a fixed end constraint was applied to the joint edges of the

supporting brackets. The force vectors that were applied along the plate were each 3 lbs. Lastly,

an incompatible mesh was created for the housing since the base plate was not realistically

supported by the perimeter of the top of the housing. By running the mesh, result plots of the

displacement, strain, and stress were outputted and shown along the different regions of the

housing.

The results computed from Solidworks revealed intriguing observations and implications.

Due to the fact that the housing held a lot of empty spaces and was made out of a hollow pipe,

the stress regions were relatively low. Only a small section of the top plate was contacting the

pipe, so a distributed force across the plate resulted in its associated cantilever beam behavior.

When the plate is deflected by an applied force from the housing along one section, then the

fixed joints of the housing will fail along the opposite end of the housing from the plate. The

displacements along the deflected ends of the strandbeest were typically on the extremely high

end of the scale, as shown below. The stress was nonexistent along the plate, except on one of

the corner edges. This stress correlated with the deflection of the structural member connected

along with that edge shown below.

Figure 45: Mesh of the Strandbeest Housing

Figure 46: Von Mises Stress of Housing

Figure 47: Resultant Strain of Housing

Figure 48: Resultant Displacement of Housing (with Applied Force)

Mechanism Kinematic and Dynamic Analysis

Since the strandbeest has many moving parts in order to provide motion, performing a

kinematic and dynamic simulation and analysis is useful to describe the motion of this

mechanism. In order to do this, a kinematic motion study was done on the legs, and a dynamic

motion study was done on the strandbeest entirely on a platform.

The kinematics was conducted by collecting data on the path the foot on the leg in order

of know its displacement and whether the feet interfere with each other which would lead to

design changes. A motor was added to the crankshaft at 12 RPM to provide the motion to the

legs. The motion study simulation was set to 5 seconds at 25 frames per second just to

demonstrate a full cycle of the motor. After running the simulation, the plots of the horizontal

linear displacement of the feet were created with the target points placed on the both on the

bottom of the feet and the reference origin at the center of the rotation of the motor. They were

then exported as .csv files and imported into MATLAB where they were both plotted on the

same figure. This plot can be seen in Figure 49. It can be shown that the feet do not interfere at

any given time, which validates this design for the legs.

Figure 49: Linear displacement of the feet of the legs vs. Time at 12 RPM

For the dynamics portion, the strandbeest was set hovering a little above near one of the

ends on a long horizontal platform (5000”x 200”). First, a motor was added to the crankshaft at a

speed of 25 RPM in order to provide motion to all 16 legs. Next, contacts were added to all of

the feet and the platform. It is important to note that the option for contact groups was chosen for

all the feet in group 1 and the platform in group 2; this was to save some computation power

when running the motion study. Adding contacts was essential for the strandbeest to perform a

walk motion across the platform in the sense that when the individual feet make contact with the

platform, the kinetic friction between them allowed for the feet to push the strandbeest forward.

Lastly, a gravitational parameter was added in the Y direction (vertical) at a value of 1g; this

ensured that the strandbeest remained on the platform and that it assisted on the contacts. This

simulation was set to run for 30 seconds at 25 frames per second. After the simulation was

finished running, plots of the horizontal linear displacement and velocity were created with the

target point placed on the housing frame and the reference origin on the corner on the end of the

platform closest to the strandbeest. They were then exported as .csv files and imported into

MATLAB for further analysis. These plots can be seen in the following pages as Figure 50 and

Figure 51. The horizontal linear displacement curve showed a trend of mostly a linear increase of

displacement with time (the beginning being a transient response); this suggested that the

strandbeest moved at a constant horizontal linear velocity. When analyzing the linear velocity

curve, the trend also seems to have a transient response at the beginning of the run which

corresponds with the linear displacement. However the trend seems to be oscillating around a

“steady state” value for velocity; this maybe explained by looking more closely at the simulation.

It could seen that throughout the run, the strandbeest seems to be slowing down and picking up

speed periodically without creating negative displacement. This could be attributed to some

unstableness to the strandbeest’s walking motion or to the design.

After analyzing the plots to check if the data was coherent, the velocity can be

calculated. The velocity that was calculated from the slope of the non-transient portion of the

linear displacement curve which came out to be 54.19 in/s. Another way to calculate the velocity

was find the mean value of the “steady state” portion of the linear velocity curve; this value came

out to be 54.1 in/s. The maximum displacement was calculated to be 1575 in.

Figure 50: Linear displacement of the strandbeest vs. Time at 25 RPM

Figure 51: Linear velocity of the strandbeest vs. Time at 25 RPM

Conclusion

The objective of this project were performing kinematic, dynamic and static stress

analysis upon a Strandbeest created and modeled within the Solidworks program.The kinematic

study was performed using a singular point on the bottom of front and back feet in the Final Leg

Assembly. This was done using linear displacement and the trace path plots to check

interferences between the links and feet during the strandbeest’s walk cycle. The dynamic

analysis was done using SolidWorks Motion Analysis tools and was completed by imposing

gravity on the model in addition to setting the solid body contact to include friction. This

frictional force between the 16 feet and the static ground is the main force in imposing dynamic

motion upon the model. The stress analysis was done using the SolidWorks Simulation tool. This

analysis provided insight into how a load applied across the top of the housing is distributed

throughout the housing.

Project Strandbeest Final Report

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