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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
Moments of inertia: ( pounds * square inches )
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
Mass = 1921.2775 pounds
Volume = 53180.7930 cubic inches
Surface area = 120066.9421 square inches
Center of mass: ( inches )
X = -74.4200
Y = -278.5196
Z = 6.1177
Principal axes of inertia and principal moments of inertia: ( pounds * square inches )
Taken at the center of mass.
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
Moments of inertia: ( pounds * square inches )
Taken at the center of mass and aligned with the output coordinate system.
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
Moments of inertia: ( pounds * square inches )
Taken at the output coordinate system.
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
Mass = 2077.55 pounds
Volume = 57372.59 cubic inches
Surface area = 136119.26 square inches
Center of mass: ( inches )
X = -74.42
Y = -276.68
Z = 6.11
Principal axes of inertia and principal moments of inertia: ( pounds * square inches )
Taken at the center of mass.
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
Moments of inertia: ( pounds * square inches )
Taken at the center of mass and aligned with the output coordinate system.
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
Moments of inertia: ( pounds * square inches )
Taken at the output coordinate system.
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.