Tensegrity Structure as the Control Base of a Flight Simulator

American Institute of Aeronautics and Astronautics

1

Tensegrity Structure as the Control Base of a Flight

Simulator

Phillip Italiano1, Cody Lafountain

2, Kelly Cohen

3, and Shaaban Abdallah

4

University of Cincinnati, Cincinnati, Ohio,45221

The aircraft industry, military, and NASA mainly rely on the Stewart platform design, a

fixed ground-based flight simulator, for the preliminary stages of pilot training and the

testing of new aircraft. These systems are large, and expensive to maintain and repair. In

this effort, we propose a Tensegrity based structural concept as the basis for a unique and

effective flight simulator. Tensegrity structures are systems of tensile cables and compressive

members. This structure has a high precision of control, is lightweight, and deployable. At

the University of Cincinnati, preliminary Tensegrity models have been constructed to test

our understanding of a dynamic nature of the system and to provide physical models to

work with. Some of these models were constructed as static models in order to gain an

understanding of construction methods. Another model was constructed as a dynamic

model, consisting of small pulleys and cables, to simulate the basic operations of a flight

simulator.

Nomenclature

θ = angular velocity about x-axis

φ = angular velocity about y-axis

ψ = angular velocity about z-axis

I. Introduction

HE main objective of this project was to use SIM Mechanics® to investigate the structural properties of a

Tensegrity flight simulator. In order to accomplish this goal, it was necessary to develop algorithms that

determine the necessary cable length variations to establish stable dynamic Tensegrity structures. These structures

were then manipulated to simulate the perturbations required to accurately simulate the characteristics of an aircraft.

Once the range of motion for a Tensegrity structure of this type was determined, the structures were subjected to

external forces to determine the dynamic responses. This system will be dynamically controlled and respond in real

time to the pilot's commands. The reasoning for this project is to design a flight simulator that could be used for

micro UAV's in wind tunnels and the replacement of conventional high-energy flight simulators.

II. Background

The concept of using tensegrity for a flight simulator developed one-step at a time, starting with an investigation

into tensegrity structures, followed by the development of a MATLAB script to generate stable tensegrity structures.

SIM Mechanics was first included as part of a student project in 2010 in an effort to begin looking at the dynamic

responses of different tensegrity structures with external force application.

A. Tensegrity Structures

Tensegrity structures are lightweight, static, and dynamic structures that are composed of compressive and

tensile members. Three dimensional static single cell structures consist of at least three compressive (bars) members,

which are axially loaded. A single cell also has at least nine tensile (cables) members, which constrain the

1 Graduate Student, School of Aerospace Systems, AIAA Student Member.

2 Graduate Student, School of Aerospace Systems, AIAA Student Member.

3 Associate Professor, School of Aerospace Systems, AIAA Associate Fellow.

4 Professor, School of Aerospace Systems, AIAA Member.

T

Infotech@Aerospace 201129 - 31 March 2011, St. Louis, Missouri

AIAA 2011-1467

Copyright © 2011 by the American Institute of Aeronautics and Astronautics, Inc. All rights reserved.

Dow

nloa

ded

by U

NIV

ER

SIT

Y O

F C

INC

INN

AT

I on

Nov

embe

r 24

, 201

4 | h

ttp://

arc.

aiaa

.org

| D

OI:

10.

2514

/6.2

011-

1467


2

compressive members and determine the stiffness of the structure. Compressive members resist both compressive

and tensile forces while maintaining their initial configuration. While tensile members are only capable of resisting

tensile forces and under compressive forces deflect and distort the initial configuration of the structure. These

compressive and tensile members can be assembled into any configuration to produce a structure. When the

structure reaches an equilibrium point, the structure becomes statically stable. A statically stable structure can stand

on its own without any external force applied. This statically structure can be combined with other structures to

produce new and more complex structures.

Complex static tensegrity structures consist of multiple single cell structures. These structures can be arranged in

any configuration and do not need to be composed of one cell configuration. The basic configuration of a tensegrity

structure is classified as a class 1 structure. Chan, W.L., and Skelton, R.E., define a class 1 structure as a strong and

lightweight structure consisting of axially loaded compressive members that do not touch and a continuous network

of pre-stressed tensile members. Pre-stressed is defined as a state where both the tensile and compressive members

receive tension and compression, respectively, forces that bring the structure into a stable equilibrium state without

any external load. An alternative classification for a tensegrity structure is called a class-k structure. Chan, W.L., and

Skelton, R.E., define a class-k structure based on the k (number) of compressive members that touch each other at a

single node.

Dynamic single cell tensegrity structures also consist of both compressive and tensile members. These members

are assembled to produce stable structures. Unlike static structures, the tensile members are either adjustable

discontinuous segments or are linked into one continuous network. The lengths of these members are manipulated to

produce movement.

Complex dynamic structures are assembled in a similar fashion as static tensegrity structures but the

configuration of the adjoining cell is taken into account. Single cells are connected so the tensile members can

interact with adjacent cells. The connections are either flexible joints or an addition of one cell’s tensile network into

the adjacent cells’ networks.

B. MATLAB Code for Stable Structure Generation

Work performed by Estrada, G.G., was used as an aid in understanding how theoretical tensegrity models are

constructed. The body of this work discusses form finding methods for generating statically stable tensegrity

structures. A primary method used in this work was tension coefficients which determined the eventual

configuration of the structure. Configuration parameters were developed to determine connection intervals between

the compression and tension members that aided in the development of statically stable structures.

Using the parameters described by Estrada, a form finding MATLAB program was developed that produced the

nodal coordinates of a static tensegrity structure. This program had to produce multiple cells and vary in size in all

directions. Once the ability to produce an initial structure had been created a plate was added to represent the flight

simulator. A rotation matrix was added to the plate which allowed the orientation of the plate to be manipulated. The

rotation matrix allowed the structure to simulate the roll, pitch, and yaw motions of an aircraft. Below the tensegrity

structure liner actuators were added to increase the range of motion that a single cell is capable of.

The MATLAB program was constructed around two concentric circles separated by an initial distance defined

by the length of the compressive members. After the basic shape was established the rotation matrix was able to

manipulate the structure while maintaining a fixed compressive member length and varying the tensile member

length. The manipulation caused the nodes on the top circle to rotate to a specified orientation. This caused the linear

actuators adjust, thus maintaining a fixed point at the center of the plate. The structure reacted in this manner for all

three motions, roll, pitch, and yaw. The coordinates for all nodes were then outputted to a file that SIM Mechanics

reads.

C. SIM Mechanics

A SIM Mechanics model was created to plot the dynamic characteristics of the tensegrity structure produced in

MATLAB. The SIM Mechanics toolbox does not include string blocks so a spring-damper was used as a substitute.

While the spring-damper block is able to simulate the tensile reaction of strings, it cannot simulate the reaction to

compression in an equal manner. The springs modeled by SIM Mechanics are bi-directional; in that, they generate

forced both when pulled in tension and when compressed.

The SIM Mechanics model consisted of four compressive members connected in manner that formed a four

sided single cell structure. This structure was connected to a base of four bodies that represented linear actuators and

a plate that the top to represent the flight simulator. At the connection points a gimbal joint was used to allow for a

completely spherical motion. Given that the structure has fixed dimensions for both the base and top allow for

Dow

nloa

ded

by U

NIV

ER

SIT

Y O

F C

INC

INN

AT

I on

Nov

embe

r 24

, 201

4 | h

ttp://

arc.

aiaa

.org

| D

OI:

10.

2514

/6.2

011-

1467


3

increased static stability. This SIM Mechanics model looked at the static stability of the tensegrity structure under

different flight simulation configurations.

A second SIM Mechanics model was created to investigate the reaction of the structure to external forces. The

physical properties of this model were set in a manner so that reasonable perturbations could be induced and damped

out within a reasonable time. Physical properties derived in this model were also used in the static model.

III. Tensegrity Flight Simulator

The proposed tensegrity flight simulator is a dynamic structure that consists of hollow bars, strong light weight

cables, pulleys, electric motors, and a simulation module. Linear actuators are a set of vertical rails and they lift the

structure by a motorized pulley system. The tensegrity structure is a system of bars, cables, and motors that control

the configuration of the structure. This system

of linear actuators and single cell tensegrity

structure forms the control base for the flight

simulator which is attached to the top of the

tensegrity structure. Alternative tensegrity flight

simulators can be constructed without the linear

actuators. These control bases consist of only

multiple tensegrity cells. The difference

between the proposed control base and the

suggested alternative is that the alternative

control base potentially has a larger range of

motion.

A. Physical Construction Advantages

Hydraulic control bases for flight simulators

require large amounts of infrastructure and need

large areas to operate in. Maintenance for

hydraulic systems is complex and component

failures cause long durations of down. Failures

in hydraulic cylinders cause fluid to leak and

the repairs to the Hydraulic fluid poses

environmental issues that require safeguards to

prevent possible contaminations and electrical

systems that power the system have to be

isolated from the fluid. Personnel must also be

protected from the high-pressure lines and the

control base.

Compared to hydraulic control bases, the use of tensegrity structures for flight simulators reduce the amount of

infrastructure needed to operate the simulation. Component failures would not shut the system down for extended

periods and replacement parts would be modular. Depending on the complexity and cost of components down time

could be limited to a few hours to replace the failed component. There would be no additional environmental issues

outside of the ones created by electricity. The only protection needed for tensegrity flight simulators would be from

the control base.

B. Static Stability

The input for the static stability model is the final set of coordinates that model the simulated flight

characteristics. SIM Mechanics takes these coordinates and creates a machine model. This machine model can

produce all possible movements and output the time response of the simulated system. The static model loads the

coordinates into a machine model and runs the simulation.

Figure 1 Theoretical Schematic

d Dow

nloa

ded

by U

NIV

ER

SIT

Y O

F C

INC

INN

AT

I on

Nov

embe

r 24

, 201

4 | h

ttp://

arc.

aiaa

.org

| D

OI:

10.

2514

/6.2

011-

1467


4

-2

0

2 -2

0

20

2

4

6

8

Linear Actuators

Bars

Cables

Plate

Figure 2 Initial Configuration

Figure 2 is the structure produced by the MATLAB program. This figure is the initial configuration of the

tensegrity flight simulator. The model produced here does not include any material properties of gravitational

influences it only provides the geometry that the SIM Mechanics needs to run a simulation.

Figure 3 SIM Mechanics Machine Model

Figure 3 is the machine model produced by SIM Mechanics. Here material properties and gravitational

influences are simulated. Gravity is applied along the z-axis and the machine model has metric units.

The following conditions will be discussed:

- Initial Configuration

- Yaw 15, -15, 90, -90, -135, -160 degrees

- Roll 45, 90 degrees

- Pitch 45, 90 degrees

- Simultaneous roll, pitch, and yaw of 45 degrees

- Horizontal displacement of 2 meters along the X-axis

- Horizontal displacement of 2 meters along the X and Y-axis

- Horizontal displacement of 2 meters along the X and Y-axis and simultaneous roll, pitch, and yaw of 45

degrees

For each simulated flight condition, measurements are taken from the center of gravity for all four bars and plate.

Both position and velocity are measured for X, Y, and Z axes. All simulated rotations are preformed keeping the

center of gravity for the plate positioned directly above the origin. During the simulated horizontal displacements the

center of gravity is allowed to move away from the origin. For the initial configuration, the position measurement

←Bar 1

←Bar 4

Bar 3→ Bar 2→

Dow

nloa

ded

by U

NIV

ER

SIT

Y O

F C

INC

INN

AT

I on

Nov

embe

r 24

, 201

4 | h

ttp://

arc.

aiaa

.org

| D

OI:

10.

2514

/6.2

011-

1467


5

for the four bars and plate showed no displacement. However, there was a small amount of disturbance measured for

the velocity component.

Figure 4 Bar Velocities for Initial Configuration

Figure 4 shows bar velocities. Here the disturbance starts out small and become negligible after five seconds.

Figure 5 Plate Velocities for Initial Configuration

Dow

nloa

ded

by U

NIV

ER

SIT

Y O

F C

INC

INN

AT

I on

Nov

embe

r 24

, 201

4 | h

ttp://

arc.

aiaa

.org

| D

OI:

10.

2514

/6.2

011-

1467


6

Figure 5 is the velocities for the plate over a fifteen-second period. Similar to the bar velocities, the plate

experienced a small disturbance that damped out after five seconds. The magnitude of velocity for both the bars and

plate is so small that the structure did not move. The only motion here is due to the input due to gravitational force

causing the structure to settle.

The first simulated flight parameters were that of yaw. A positive yaw of 15 degrees was simulated, unlike the

initial condition, the position measurement showed a small amount of displacement in the X and Y direction.

However, the displacement measured depicted a small settling motion where the structure shifted slightly and came

to rest.

Figure 6 yaw 15 degrees

Dow

nloa

ded

by U

NIV

ER

SIT

Y O

F C

INC

INN

AT

I on

Nov

embe

r 24

, 201

4 | h

ttp://

arc.

aiaa

.org

| D

OI:

10.

2514

/6.2

011-

1467


7

Figure 7 yaw 15 degrees

Next, a yaw of 90 degrees was simulated. Figure 8 indicates that a yaw 90 degrees is the limit for yaw motion in

the positive direction. This configuration causes the cables to intersect at the center of the structure and prevents any

additional positive rotation. Thus, the final rotation in the positive direction is determined by the diameter of the

cables used.

-3

-2

-1

0

1

2

3 -3

-2

-1

0

1

2

3

0

1

2

3

4

5

6

7

8

9

Figure 8 structural configuration for a yaw of 90 degrees

A yaw of 90 degrees has a similar positional measurement and magnitude as a yaw of 15 degrees. Unlike the 15

degree yaw, the 90-degree yaw now experiences some position along the Z-axis. Additionally the magnitude of the

velocities for the bars and plate are much larger than the 15-degree velocities.

Dow

nloa

ded

by U

NIV

ER

SIT

Y O

F C

INC

INN

AT

I on

Nov

embe

r 24

, 201

4 | h

ttp://

arc.

aiaa

.org

| D

OI:

10.

2514

/6.2

011-

1467


8

Figure 9 bar velocities for a yaw of 90 degrees

Figure 10 plate velocities for a yaw of 90 degrees

The increase in magnitude of oscillation for both position and velocity indicates an increase of instability within

the structure.

Dow

nloa

ded

by U

NIV

ER

SIT

Y O

F C

INC

INN

AT

I on

Nov

embe

r 24

, 201

4 | h

ttp://

arc.

aiaa

.org

| D

OI:

10.

2514

/6.2

011-

1467


9

Next yaw was simulated in the negative direction. The first simulated yaw was at -15 degrees. Exactly like the

yaw of 15 degrees, the -15 degree yaw had no measured positional oscillation. The only difference was the value of

the positions. Here the -15 degree yaw differs from the 15-degree yaw in velocity.

Figure 11 bar velocities for a yaw of -15 degrees

Dow

nloa

ded

by U

NIV

ER

SIT

Y O

F C

INC

INN

AT

I on

Nov

embe

r 24

, 201

4 | h

ttp://

arc.

aiaa

.org

| D

OI:

10.

2514

/6.2

011-

1467


10

Figure 12 plate velocities for a yaw of -15 degrees

The next simulated yaw was at -90 degrees. Again, the position measurements for the bars and plate are similar

to the previous yaw simulations. In this configuration, there is a measured positional oscillation but the magnitude is

small and the structure damps out the oscillation.

Dow

nloa

ded

by U

NIV

ER

SIT

Y O

F C

INC

INN

AT

I on

Nov

embe

r 24

, 201

4 | h

ttp://

arc.

aiaa

.org

| D

OI:

10.

2514

/6.2

011-

1467


11



The next simulated yaw was at -135 degrees. Unlike all previous yaw configurations, the -135 degree yaw has a

significant positional oscillation. This configuration does not damp out the oscillation until after ten seconds.

Dow

nloa

ded

by U

NIV

ER

SIT

Y O

F C

INC

INN

AT

I on

Nov

embe

r 24

, 201

4 | h

ttp://

arc.

aiaa

.org

| D

OI:

10.

2514

/6.2

011-

1467


12

Figure 15 bar positions for a yaw of -135 degrees

Figure 16 plate positions for a yaw of -135 degrees

The velocities for each member is also much larger compared to the previous yaw configurations. This

configuration has much larger oscillation amplitudes and takes longer to damp out.

Dow

nloa

ded

by U

NIV

ER

SIT

Y O

F C

INC

INN

AT

I on

Nov

embe

r 24

, 201

4 | h

ttp://

arc.

aiaa

.org

| D

OI:

10.

2514

/6.2

011-

1467


13



The last yaw configuration is at -160 degrees. Excluding the yaw of -135 degrees, this configuration has similar

position measurements as the previous yaw configurations. This configuration approaches the limit of the yaw

Dow

nloa

ded

by U

NIV

ER

SIT

Y O

F C

INC

INN

AT

I on

Nov

embe

r 24

, 201

4 | h

ttp://

arc.

aiaa

.org

| D

OI:

10.

2514

/6.2

011-

1467


14

rotation in the negative direction. The structural limit is due to that bar intersection at the center of the structure and

an additional limit comes from the SIM Mechanics machine model. In the SIM Mechanics model any yaw greater

than -160 degrees collapses under its own weight and the simulation fails.

Figure 19 structural configuration for a yaw of -160 degrees


Dow

nloa

ded

by U

NIV

ER

SIT

Y O

F C

INC

INN

AT

I on

Nov

embe

r 24

, 201

4 | h

ttp://

arc.

aiaa

.org

| D

OI:

10.

2514

/6.2

011-

1467


15


The next set of flight configurations involves roll simulations. Configurations describe below only involve rolls

of 45 and 90 degrees. Rolls of -45 and -90 degrees react in a similar manner as the positive rolls just in the negative

direction. The first simulated roll is at 45 degrees. Like the yaw motion, for a roll of 45 degrees there is no measured

position oscillation for the bars and plates. There are some velocity oscillations in the bars and plate.

Dow

nloa

ded

by U

NIV

ER

SIT

Y O

F C

INC

INN

AT

I on

Nov

embe

r 24

, 201

4 | h

ttp://

arc.

aiaa

.org

| D

OI:

10.

2514

/6.2

011-

1467


16

Figure 22 bar velocities for a roll of 45 degrees

Figure 23 plate velocities for a roll of 45 degrees

The second simulated roll is at 90 degrees. This configuration reacts in a similar fashion as the previous roll.

There is no measured positional oscillation and unlike the 45 degree roll, the velocity oscillation damps out within

Dow

nloa

ded

by U

NIV

ER

SIT

Y O

F C

INC

INN

AT

I on

Nov

embe

r 24

, 201

4 | h

ttp://

arc.

aiaa

.org

| D

OI:

10.

2514

/6.2

011-

1467


17

five seconds. A physical limit arises here due to the intersection of the plate with one of the cables. Thus, the

simulated roll is limited to the thickness of the plate and the diameter of the cable. The following figure indicates

that a cable is in front of the plate but in fact, the plate and cable are overlapping.

Figure 24 structural limit for a roll of 90 degrees

Figure 25 bar velocities for a roll of 90 degrees

Dow

nloa

ded

by U

NIV

ER

SIT

Y O

F C

INC

INN

AT

I on

Nov

embe

r 24

, 201

4 | h

ttp://

arc.

aiaa

.org

| D

OI:

10.

2514

/6.2

011-

1467


18


The third simulated flight parameter is for pitches of 45 and 90 degrees. Similar to the simulated rolls the pitches

in the negative direction react in a similar manner as their positive counter parts. The first simulated pitch is at 45

degrees. For this configuration, there was no measured positional oscillation. Like the simulated rolls this pitch’s

velocity, oscillations start with small magnitudes and are completely damped out after five seconds.

Figure 27 bar velocities for a pitch of 45 degrees

Dow

nloa

ded

by U

NIV

ER

SIT

Y O

F C

INC

INN

AT

I on

Nov

embe

r 24

, 201

4 | h

ttp://

arc.

aiaa

.org

| D

OI:

10.

2514

/6.2

011-

1467


19

Figure 28 plate velocities for a pitch of 45 degrees

For the second and final pitch is simulated at 90 degrees. This configuration reacts in a similar fashion as the

previous pitch but the simulation takes much longer to damp out its velocity oscillations. There is also no measured

positional oscillation. Like the simulated roll, a pitch of 90 degrees is at the physical limit of rotation, which is due

to the intersection of the plate with one of the cables. Thus, the simulated pitch is limited to the thickness of the plate

and the diameter of the cable.

Figure 29 bar velocities for a pitch of 90 degrees

Dow

nloa

ded

by U

NIV

ER

SIT

Y O

F C

INC

INN

AT

I on

Nov

embe

r 24

, 201

4 | h

ttp://

arc.

aiaa

.org

| D

OI:

10.

2514

/6.2

011-

1467


20


The last rotational flight parameter involves a simultaneous roll, pitch, and yaw of 45 degrees. Like most

previous flight parameters, there is no measured positional oscillation. No further investigation was conducted to

find the limits of this configuration because the limits are defined in the separate roll, pitch, and yaw simulations.

Figure 31 bar velocities for a roll, pitch, and yaw of 45 degrees

Dow

nloa

ded

by U

NIV

ER

SIT

Y O

F C

INC

INN

AT

I on

Nov

embe

r 24

, 201

4 | h

ttp://

arc.

aiaa

.org

| D

OI:

10.

2514

/6.2

011-

1467


21

Figure 32 plate velocities for a roll, pitch, and yaw of 45 degrees

For the final set of simulated flight parameters involves horizontal displacement and the combination of

horizontal displacement and a simultaneous roll, pitch, and yaw of 45 degrees. The first horizontal displacement is

two meters in the positive X direction. This configuration produces some measurable position oscillation but the

magnitudes are small and damp out within five seconds. However, the velocities are much larger and take at least

ten seconds to damp out.

Figure 33 bar velocities for a displacement of 2 meters along the X-axis

Dow

nloa

ded

by U

NIV

ER

SIT

Y O

F C

INC

INN

AT

I on

Nov

embe

r 24

, 201

4 | h

ttp://

arc.

aiaa

.org

| D

OI:

10.

2514

/6.2

011-

1467


22

Figure 34 plate velocities for a displacement of 2 meters along the X-axis

The second simulated configuration involves a displacement of two meters in both the X and Y directions. This

configuration responds in a similar manner as the previous displacement but the position measurements are slightly

larger but still have small magnitudes and damp out with in ten seconds. The velocities for this simulation are very

similar to the previous simulation as well.

Figure 35 bar velocities for a displacement of 2 meters along the X and Y-axes

Dow

nloa

ded

by U

NIV

ER

SIT

Y O

F C

INC

INN

AT

I on

Nov

embe

r 24

, 201

4 | h

ttp://

arc.

aiaa

.org

| D

OI:

10.

2514

/6.2

011-

1467


23

Figure 36 plate velocities for a displacement of 2 meters along the X and Y-axes

The final static simulation involves a combination of horizontal displacement and a simultaneous roll, pitch, and

yaw of 45 degrees. This simulation combines the final rotational configuration and the second simulated horizontal

displacement. Reactions to this configuration are similar to the simulated displacements in X and Y. Positional

measurements are slightly larger than the previous simulation but are still small and damp out within 10 seconds.

Figure 37 bar velocities for a displacement of 2 meters along the X and Y-axes and a roll, pitch, and yaw of 45

degrees

Dow

nloa

ded

by U

NIV

ER

SIT

Y O

F C

INC

INN

AT

I on

Nov

embe

r 24

, 201

4 | h

ttp://

arc.

aiaa

.org

| D

OI:

10.

2514

/6.2

011-

1467


24

Figure 38 plate velocities for a displacement of 2 meters along the X and Y-axes and a roll, pitch, and yaw of

45 degrees

Displacements in a vertical direction were not investigated. Vertical displacements are achieved several ways.

Manipulating the linear actuators achieves vertical displacements; alternatively the linear actuators are fixed and a

yaw motion is performed.

Knowing the lengths of all cables and displacement of the linear actuators, control laws can be derived to control

the shape of the structure. Table 1 lists the lengths of each member that is capable of changing its shape.

Table 1 member lengths Configuration Member Lengths (m)

Initial Cable 4.24 4.24 4.24 4.24

7.35 7.35 7.35 7.35

Linear Actuator 3 3 3 3

Yaw 15 Cable 4.24 4.24 4.24 4.24

7.62 7.62 7.62 7.62

Linear Actuator 3.05 3.05 3.05 3.05

Yaw 90 Cable 4.24 4.24 4.24 4.24

7.35 7.35 7.35 7.35


Yaw -15 Cable 4.24 4.24 4.24 4.24

6.98 6.98 6.98 6.98


Yaw -90 Cable 4.24 4.24 4.24 4.24

4.24 4.24 4.24 4.24


Yaw -135 Cable 4.24 4.24 4.24 4.24

3.25 3.25 3.25 3.25


Yaw -160 Cable 4.24 4.24 4.24 4.24

3.59 3.59 3.59 3.59


Roll 45 Cable 4.74 4.74 4.74 4.74

5.75 5.34 9.16 8.91

Linear Actuator 5.12 3 0.88 3

Dow

nloa

ded

by U

NIV

ER

SIT

Y O

F C

INC

INN

AT

I on

Nov

embe

r 24

, 201

4 | h

ttp://

arc.

aiaa

.org

| D

OI:

10.

2514

/6.2

011-

1467


25

Roll 90 Cable 5.2 5.2 5.2 5.2

5.2 4.24 9.95 9.49

Linear Actuator 6 3 0 3

Pitch 45 Cable 4.77 4.77 4.71 4.71

8.91 5.71 5.34 9.11

Linear Actuator 3 5.19 3 0.94

Pitch 90 Cable 5.7 5.7 4.78 4.78

9.49 4.78 4.24 9.23

Linear Actuator 3 6.8 3 0.8

Roll, Pitch, Yaw 45 Cable 4.35 5.81 4.25 5.35

8.12 4.73 7.15 10.18


Displace X Cable 4.24 4.24 4.24 4.24

6.48 8.12 8.12 6.48


Displace X and Y Cable 4.24 4.24 4.24 4.24

5.48 7.35 8.83 7.35


Displace X, Y and

Roll, Pitch, Yaw 45 Cable 4.45 5.62 4.27 5.13

6.7 5.6 8.54 9.73


This information can be used in method as the work done by Corless, Skelton, and Sultan. The work performed

by these authors was to investigate feasibility of tensegrity structures as the control base for a flight simulator. Their

primary work was focused the use of nonlinear controllers that are capable of achieving robust tracking for any

desired motion. The approach taken by the authors requires the derivation of second order nonlinear ordinary

differential equations to describe the motion of the tensegrity flight simulator. Whereas the work performed in this

paper does not require the derivation of any equations of motion.

C. Dynamic Responses

The dynamic model like the static model takes the final set of coordinates from MATLAB and loads them into

SIM Mechanics which creates a machine model. This machine model represents all possible movements and outputs

the time response of the simulated system. Here the dynamic model runs the simulation with the same initial

parameters as the static model but also includes an external force applied to the center of the plate. In all dynamic

simulations the applied external force is defined in the SIM Mechanics model as three step inputs of -2 Newtons in

the X, Y, and Z directions. The following conditions will be discussed:

- Initial Configuration

- Yaw 15, -15, 90, -90, -135 degrees

- Roll 45, 90 degrees

- Pitch 45, 90 degrees

- Simultaneous roll, pitch, and yaw of 45 degrees

- Horizontal displacement of 2 meters along the X-axis

- Horizontal displacement of 2 meters along the X and Y-axis

- Horizontal displacement of 2 meters along the X and Y-axis and simultaneous roll, pitch, and yaw of 45

degrees

Following the same pattern as the static models there is only as small amount of positional oscillation measured

in the initial configuration which damps out within five seconds. As expected the velocities of the members are

much larger and unlike the static model, the velocities for the bars react the same way as the plate so the bar velocity

plots are omitted.

Dow

nloa

ded

by U

NIV

ER

SIT

Y O

F C

INC

INN

AT

I on

Nov

embe

r 24

, 201

4 | h

ttp://

arc.

aiaa

.org

| D

OI:

10.

2514

/6.2

011-

1467


26

Figure 39 plate velocities for the initial configuration

The next simulated flight parameters are for yaw configurations. For a yaw 15 degrees there is some oscillation

in positions but the magnitudes are small and damp out within five seconds.


Dow

nloa

ded

by U

NIV

ER

SIT

Y O

F C

INC

INN

AT

I on

Nov

embe

r 24

, 201

4 | h

ttp://

arc.

aiaa

.org

| D

OI:

10.

2514

/6.2

011-

1467


27

Next is yaw of 90 degrees. The position oscillation for this configuration is more pronounced that the previous

yaw but is damped out after five seconds. The amplitude of the oscillations for the bar velocities are reduced by half

after five seconds and then approach zero after ten seconds.


The next simulated yaw is at -15 degrees. Oscillation in position for the members is smaller than the 15-degree

yaw configuration and responds in a similar manner.


Dow

nloa

ded

by U

NIV

ER

SIT

Y O

F C

INC

INN

AT

I on

Nov

embe

r 24

, 201

4 | h

ttp://

arc.

aiaa

.org

| D

OI:

10.

2514

/6.2

011-

1467


28

The next simulated yaw is at -90 degrees. Oscillations in position are experienced along the Z axis. Velocity

responses for the bars have a similar shape as the plate but damp out after four seconds.


The final yaw is at -135 degrees. The largest position oscillation is experienced in this configuration and takes

fifteen seconds to damp out. Bar velocities react in a similar manner as the plate but experience oscillations along all

three axes.


Dow

nloa

ded

by U

NIV

ER

SIT

Y O

F C

INC

INN

AT

I on

Nov

embe

r 24

, 201

4 | h

ttp://

arc.

aiaa

.org

| D

OI:

10.

2514

/6.2

011-

1467


29

The last yaw of -160 degrees simulated in the static stability section cannot be simulated in this section. During

the simulation run for the -160 degree yaw, the external force caused the bars to cross and the machine model

produced errors stating a violation of physical constraints.

The next set of simulated flight parameters is for rolls of 45 and 90 degrees. For the first simulated roll at 45

degrees, three bars and the plate experience positional oscillation along the X axis. The bars have a similar velocity

response as the plate and damp out at the same time.


The final roll is at 90 degrees. Responses for all members are similar to the roll of 45 degrees but with a smaller

magnitude.


Dow

nloa

ded

by U

NIV

ER

SIT

Y O

F C

INC

INN

AT

I on

Nov

embe

r 24

, 201

4 | h

ttp://

arc.

aiaa

.org

| D

OI:

10.

2514

/6.2

011-

1467


30

The third set of rotations is for pitches of 45 and 90 degrees. Responses for members in this configuration are

similar to the roll configurations but in different axes.


The last pitch is at 90 degrees.


Dow

nloa

ded

by U

NIV

ER

SIT

Y O

F C

INC

INN

AT

I on

Nov

embe

r 24

, 201

4 | h

ttp://

arc.

aiaa

.org

| D

OI:

10.

2514

/6.2

011-

1467


31

The final set of rotations is for a simultaneous roll, pitch, and yaw of 45 degrees. Positional oscillations for each

member are experienced along the X and Y-axis and damp out after five seconds.

Figure 49 simultaneous roll, pitch, and yaw of 45 degrees

The next set of simulated flight parameters is for horizontal displacements. The first horizontal displacement is

two meters along the positive X-axis. Similar to the previous simulated flight parameter positional oscillation is

experienced along the X and Y-axis. Bar velocities respond in a similar manner as the plate.

Figure 50 horizontal displacement along the X-axis

Dow

nloa

ded

by U

NIV

ER

SIT

Y O

F C

INC

INN

AT

I on

Nov

embe

r 24

, 201

4 | h

ttp://

arc.

aiaa

.org

| D

OI:

10.

2514

/6.2

011-

1467


32

The second horizontal displacement is two meters along both the X and Y-axis. The members in this

configuration experience some oscillation in position but the oscillation is damped out after seven seconds. Bar

velocities have a similar shape as the plate and damp out at the same rate.

Figure 51 plate velocities for a displacement along the X and Y-axis

The final simulated flight parameter is for a displacement of two meters along the X and Y-axis and

simultaneous roll, pitch, and yaw of 45 degrees. Positional oscillation is similar to the two previous displacement

simulations and the bar velocities have a similar trend as the plate.

Figure 52 plate velocities for a displacement along the X and Y-axis and simultaneous roll, pitch, and yaw of

45 degrees

Dow

nloa

ded

by U

NIV

ER

SIT

Y O

F C

INC

INN

AT

I on

Nov

embe

r 24

, 201

4 | h

ttp://

arc.

aiaa

.org

| D

OI:

10.

2514

/6.2

011-

1467


33

IV. Conclusion

The Tensegrity Flight Simulator has the capacity to reduce complexity and cost in a ground based flight

simulator. Through the use of electric cable actuators a Tensegrity system might be developed which can provide the

full required range of motion with significantly reduced repair costs. Tensegrity structures can be useful in many

applications. They have the capacity to provide great weight savings over traditional structures. As some dynamic

problems are prohibitively difficult to solve by hand, the advent of new modeling technologies such as SIM

Mechanics has made dynamic systems analysis and design much easier and less time consuming. Though SIM

Mechanics does have its drawbacks, it is still a powerful tool for solving multi-body dynamics problems. It allows

one to avoid the lengthy process of deriving the equations of motion by hand and can provide in seconds visual

simulation of a dynamic system that would take many hours to solve conventionally. Further analysis into this area

of research is suggested.

References 1Chan, W.L., Skelton, R.E., "Equilibria and Stiffness of Planar Tensegrity Structures," AAS/AIAA Space Flight Mechanics

Meeting, San Antonio, Texas, January 2002. 2Corless, M., Skelton, R.E., Sultan, C., "Tensegrity Flight Simulator," Journal of Guidance, Control, and Dynamics, Vol. 23,

No. 6, November-December 2000. 3Estrada, G.G., "Analytical and numerical investigations of form-finding methods for tensegrity structures," Max-Planck-

Institut fur Metellforschung und Universitat Stuttgart, 2007. 4Gallagher, R.H., McGuire, W., Ziemian, R.D., Matrix Structural Analysis, 2nd ed., John Wiley and Sons, Inc., 2000. 5Masic, M., Skelton, R.E., "Open Loop Control of Class 2 Tensegrity Structures," SPIE's 11th Annual International

Symposium on Smart Structures and Materials, San Diego, Ca, March 2004.

Dow

nloa

ded

by U

NIV

ER

SIT

Y O

F C

INC

INN

AT

I on

Nov

embe

r 24

, 201

4 | h

ttp://

arc.

aiaa

.org

| D

OI:

10.

2514

/6.2

011-

1467

Tensegrity Structure as the Control Base of a Flight Simulator

Documents

Transcript of Tensegrity Structure as the Control Base of a Flight Simulator