Statically balancing using an elastic actuator that is efficiently adjustable in all positions

119 Pages·2013·9.47 MB·English

Statically balancing using an elastic
actuator that is efficiently adjustable in
all positions

The Master Thesis of:

Jesse van Dongen

Delft University of Technology
Faculty of Mechanical, Maritime and Materials Engineering
Department of BioMechanical Engineering

Student Number: 1316125
Master Exam: Excie034-2013

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Preface
This report shows my master exam paper on statically balancing using an elastic actuator that is efficiently
adjustable in all positions. The results discuss the possibility of balancing a pendulum without a fixed
vertical reference. Over the last year I learned a lot regarding building and creating prototypes, and
searching and reading through scientific literature. It seems that a paper never feels completely finished,
and if I could I would like to create a whole new second prototype and continue till everything is deemed
perfect (if it ever is). This shows that even with a single assignment that the time always goes by quicker
than you think.

I would like to thank Just Herder from TUdelft , together with everybody at InteSpring BV (especially
Giuseppe Radaelli ,Emile Rosenberg and my supervisor Milton Aguirre) for their support in guiding me
through the steps of my master thesis. Finally I would like to thank my exam committee for their patience
with me handing in my report. Writing has never been my strongest asset, making the creation of this
paper a big struggle for me, however I hope that I will take the readers on a pleasant and interesting
journey.

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CONTENTS
Statically balancing using an elastic actuator that is efficiently adjustable in all positions1
Abstract ..................................................................................................................................................... 1
Nomenclature ............................................................................................................................................ 1
1. Introduction ........................................................................................................................................... 1
2. Method .................................................................................................................................................. 2
Detailed Problem Description: Balancers Without Fixed Reference ..................................................... 2
Requirements For Functioning .............................................................................................................. 2
Desires For Competitiveness ................................................................................................................. 3
Overview of the criteria and desires ..................................................................................................... 3
Main Process Diagram ........................................................................................................................... 3
Subdivision Into Energy Storage And Transfer ...................................................................................... 4
Design And Prototype............................................................................................................................ 4
Experimental Evaluation........................................................................................................................ 6
3. Results ................................................................................................................................................... 9
Transmission Performance .................................................................................................................... 9
Performance Of the Force Adjustment Slider ....................................................................................... 9
Force Losses Breakdown ..................................................................................................................... 10
4. Discussion ............................................................................................................................................ 11
5. Conclusion ........................................................................................................................................... 11
Acknowledgments ................................................................................................................................... 12
References ............................................................................................................................................... 12
Appendices .............................................................................................................................................. 15

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Department of Mechanical Engineering, Faculty of Mechanical, Materials and Maritime Engineering
BMechE
July 11, 2013, Delft, Netherlands
Excie034-2013
STATICALLY BALANCING USING AN ELASTIC ACTUATOR THAT IS EFFICIENTLY
ADJUSTABLE IN ALL POSITIONS

Jesse van Dongen
Department of Mechanical Engineering, Faculty of
Mechanical, Materials and Maritime Engineering,
Delft University of Technology
Delft, The Netherlands
Email: [email protected]

ABSTRACT 1. INTRODUCTION
Technologies exist that equilibrate the effects of gravity; Recent developments showcase an increased interest in
however there are limitations to these technologies. Spring energy efficient actuation. For example, vehicles are being
based gravity equilibrators require an always present vertical equipped with Kinetic Energy Recovery Systems [1-3], and
reference, while in some cases, like on devices worn on the within the field of Robotics there is a search for actuators with
human body there is no part that is always vertical. recoverable energy [4-6]. Both in the field of Robotics and
The goal of this paper is to conceptualize, build and Prosthetics, gravitational forces generate a high energy cost to
evaluate a regenerative elastic actuator that can adjust its accomplish simple tasks, such as holding an object in space.
output force efficiently at any position, for the application of Technologies like statically balancing exist, which
gravity equilibration. effectively equate the effect of gravity within a system;
A concept and eventual prototype was realized by adjusting although current methods have various considerations and
perpendicular to the driving force, and dividing the problem limitations that need to be taken into account. One of those
into many sub problems. Results showcased, that the output limitations, in the special case of spring based balancers, is the
force could be changed at any position, with the adjustment requirement of an always present fixed vertical reference [7]. A
force being separated at the exception of friction. second limitation lies in the energy efficient adjustability of
Showcasing that it is possible to create an elastic actuator such systems 1.
that is adjusted efficiently at any position, allowing for systems One application where a consistent vertical reference is not
to be gravity equilibrated that otherwise cannot be. available is in the case of balancing on a non-fixed base, such
as a human. In this example, this limits the utilization and
NOMENCLATURE functionality of spring balanced devices when used for
x position of the adjustment system [mm] exoskeletons and other systems where the base can change its
 deviation of a pendulum with the gravity orientation.
vector [deg] Similarly energy efficient adjustability at any moment or
µ mean value position, allows for the creation of a “Very Versatile Energy
ơ standard deviation Efficient” actuator that is able to store energy for any force
F_out output force of the system [N] profile generating negative work on the load [4].
F_out_min minimum output force of the system [N] The goal of this paper is to design and evaluate an energy
F_out_max maximum output force of the system [N] efficient elastic actuator (an actuator that utilizes an elastic
F_weight weight times the gravity constant [N] energy source) capable of efficiently changing its stiffness
 energy efficiency [%]

s slip [%]
1 A literature search (See Appendix O) found systems that could be energy
t time [s]
efficiently adjusted at a single position, systems that could be energy efficiently
adjusted when locked, but only 3 systems that could be energy efficiently
adjusted in all positions. See appendix X
1
profile demonstrated by the example of statically balancing a
pendulum on a sloped surface. A similar issue occurs with balancing systems that can be
This paper will present a short introduction to the problem worn on the human body. A patent from Agrawal et al [10]
of statically balancing without a fixed reference, followed by a balances the weight of a human’s leg, the orientation of the
problem analysis and subdivision. This generates requirements, torso is used as a vertical reference, meaning that if the torso is
for the design and creation of a prototype, which will be built no longer straight up (e.g. bending forward) the device will no
evaluated and discussed. longer show the desired behavior of balancing the leg. As there
is no part of the human body that is always vertical, currently
having a spring balanced device that always balances correctly
2. METHOD requires a connection to the outside world as seen in the patent
Detailed Problem Description: Balancers Without of Ou Ma et al [11].
Fixed Reference In general the advantages of a spring balanced system are
When operating a device against external forces, such as often desired in applications where size, inertia or total mass
those induced by gravity there will be energy costs. Balancing play an important role. Similar criteria are often desired in
methods have been created to negate the influence of external systems that need to be able to move or be transported, and it is
forces on a system, lowering the operating energy costs of the exactly those devices that often do not have a fixed reference to
system. the ground. This creates the demand for a spring balanced
Two common methods to balance a system against gravity system that can still operate without fixed reference.
are balancers based on counterweights or spring mechanisms With an understanding of the problem, it becomes
(See appendix A for more details) important to define the design criteria. These are based on the
While spring based balancers offer some big advantages requirements for the device to function and the ability for the
over counterweight systems with regard to the systems overall device to be competitive against other balancing methods.
size and weight, they require a fixed vertical gravity reference.
For example, in systems with multiple degrees of freedom,
like adding pendula in series, when balanced with springs, a Requirements For Functioning
mechanism needs to be attached that passes through the Comparing the required moments of an inverted pendulum
reference of the gravity orientation for each individual pendula. starting in an upright position relative to the ground on both a
The most common solution utilizes four-bar mechanisms [8]. horizontal and slanted surface (figure 2) it can be seen that the
Systems exist that work by balancing the effective center required sinusoidal balancing torque encounters a phase shift
of mass (referenced through a bar linkage) [9]. However those with respect to the ground. Notice that the moment curve of the
systems still require a lot of parts when compared to mass pendulum relative to gravity direction remains unchanged.
balanced pendula, which can simply be stacked. With the possibility of a phase shift between 0 and 90° (for
Secondly, in systems where there is no location fixed instance mounting the pendulum on a vertical wall instead of
relative to the gravity vector, a new problem surfaces as there is on the ground),for any angle between the arm of the pendulum
no longer a direct location the balancer can be fixed to. An and the ground surface, the applied torque should be able to
example of such a case is displayed in Figure 1, while a vary from the minimal torque to the maximal torque.
counterweight based balancer will continue to function when This generates the first desired property:
the base is rotated, a spring based balancer will lose its
orientation with respect to gravity and lose its ability to 1) At any position the balancer should be able to change
balance. between the minimal and maximal torque.

figure 2. Showcase of the required moments of an inverted

pendulum at various positions relative to the ground
Figure 1. A showcase of a counterweight and spring based
underneath. On the left the case with a level ground is
balancer when the base is rotated. As the base is a reference
depicted, while on the right the case with a slanted surface
for the direction of gravity for a spring based balancer, it
is presented, the slanted surface showcases the need for a
will stop functioning when the base is rotated.
phase shift in the effective balancing force.

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Table 1. Requirements for the system
Desires For Competitiveness
Property Requirement
The first main desire concerns one of the main advantages
Ability for adjustment ∀ x ∈ [x ,x ]
for statically balanced systems; the low force and energy min max

requirements for operation.

If a statically balanced system would require big (energy
Table 2. Desires of the prototype
consuming and heavy) actuators to adjust the system, it would
Property Desire
undo its advantages. From which follows, that ideally the
adjustment mechanism should adjust the applied torque without Total efficiency  >75%
any energy cost. This leads to the main desire for such a Slip s = 0%
system: Adjusting output force Corr(F_Adjust,F_output) = 0
Adjusting output force F_Adjust << F_output_max
1) Changing the torque should be energy efficient and Total weight F_weight < F_out_max
ideally force free 2 Output range ∠  > 90°
min max
2) The total system should be able to energy efficiently
Gear Ratio adjustment F_out_max/F_out_min > √2
withdraw and store energy
Ability to change profile f () <>= f ()
x t=0 x t=1

The major advantage of a spring based balancer over a

counterbalanced system is the size and weight. Therefor unless
Main Process Diagram
the device can continue to compete on these fields, the use of
In order to break down the design problem into multiple
simpler counterbalanced system would always be preferred,
sub problems, the system was investigated using a closed
generating the second desire for such a system.
feedback loop (Figure 3).

The total system was separated into 4 parts. The first part is
3) The weight of the system should be smaller than the
an actuator that provides (or receives) energy from the
total balanced weight.
pendulum when it changes its relative angle towards gravity.

The second part is the pendulum itself. The third component is
The final desire stems from the assumption that the system
a sensor (electrical or mechanical) that measures the angle of
will likely become more complex and expensive than
the pendulum relative to the gravity vector. This device
traditional methods of balancing. If the system is able to adjust
transfers the information of the pendulum to the fourth part; the
the force output at any time, it would be nice if this could be
controller that based on the angle of the pendulum provides the
utilized to not only change the phase of the balancing function
correct actuator setting to keep the pendulum balanced.
but amplitude and shape as well. So that possible increases in
complexity and cost could be covered by adaptability and
added functionality of such a device.

4) Ability of adjustment of the balancing force at any
point.

With the main property and desires defined, an overview
can be generated, showcasing measurable design parameters.

Overview of the criteria and desires Figure 3. Closed loop block diagram showcasing a
Based on requirements and desires for the elastic actuator, breakdown of components for balancing a pendulum using
and overview in Table 1 and Table 2 has been constructed. an elastic actuator. Double lines near the pendulum indicate
The total efficiency is based on a personal desire to have an the ability for the pendulum to provide and obtain energy to
efficiency that is higher than most electric energy recovery and from the actuator.
devices. Slip is set at 0% to ensure no leakage from the energy
storage. The gear ratio and range were added to the list to allow
a pendulum to be offset 45° from a horizontal position for Both the sensor and controller could be mechanical or
demonstrative purposes. electrical; however the necessary controller and sensor depend
on the functioning of the elastic actuator. As the actuator is the
most critical component it was further broken down, into

2 A note should be made that a restriction exists on the ability to freely subdivisions.
change the torque at any position without any energy costs. The average work
done by the pendulum should remain zero, as otherwise the search for a
perpetual motion device would be initiated.
3
Subdivision Into Energy Storage And Transfer  Lever CVT3 based stiffness actuators [33-39]
To break down the complexity of the elastic actuator its  Other CVT3 based stiffness actuators [40]
functioning is separated in 2 parts, Energy Storage and Energy
Transfer (Figure 4). Within these categories the category of changing the
The energy storage holds a buffer of energy that stores energy storage through a CVT3 showcased the most variety in
energy when the pendulum loses some of its potential energy, technologies that could be utilized for energy efficient
and releases energy when the pendulum needs to gain potential adjustment while under load. For this reason only the field of
energy. The Energy transfer ensures that the energy from the adjustable transmissions was used for concept generation.
Energy storage reaches the pendulum and vice versa.
To change the output towards and away from the
pendulum, either the energy storage or the energy transfer need
to change their throughput (Figure 4). To generate an overview
of the possibilities, a search on literature has been conducted on
these elements.

Figure 5: a simple demonstration of the separation in
energy storage and energy transfer for a simple mechanism
of a lever attached to a spring that follows hooke’s law . The
energy storage defines the spring stiffness (k) affecting the
force generated for a certain spring deflection (δx) (in the
Figure 4. Zoom in on the actuator block of the closed loop figure the red spring element), while the energy transfer
block diagram, depicting a separation in energy storage and determines the amount of actual spring deflection (δx)
energy transfer as possible methods for altering the output based on an input displacement (u) (in the figure the green
torque. lever element).

As this papers focus is on an elastic actuator, only the
utilization of elastic elements for energy storage was Design And Prototype
investigated (See appendix B). When using an elastic material With a defined set of criteria and desires, and a possible
as energy storage, the amount of energy stored is a function of solution field for adjustability, concepts were generated. As all
the deformation and the material & geometric properties that concepts follow the block scheme of Figure 3, for the sake of
give the energy storage element its stiffness. This generates the simplicity the final concept will be discussed based on the
notion that the Energy Storage can be controlled by regulating individual parts for the block scheme. The order of discussion
the effective stiffness of the storage, and that the Energy will be about the energy transfer, energy storage, and finally the
Transfer can be controlled by changing and controlling the sensor and controller.
actual deformations applied on the elastic material (Figure 5).

Energy Transfer.
Categories Of Adjustable Systems. Three concepts were generated for the function of altering
A search on literature (See Appendix O) allowed for the the apparent output stiffness (Figure 6). 1.the Omniwheel CVT
creation of the following subdivision. Systems that adjust the mechanism, 2.the Ball CVT mechanism and finally 3. The
energy container can be grouped in the following categories Adjustable bar-linkage. For the used morphological table to
 Devices that adjust the pretension of a system [12-18] generate the concepts please see Appendix N.
 Devices that change the active part of the spring The omniwheel CVT mechanism showcases 2 friction
element [19-24] wheels (Figure 6 Top), changing the radius where the small
 Devices that change how the system is loaded [25, 26] wheel sits on the big wheel changes the transmission ratio.
Systems for changing the transmission ratio can be grouped in However by using an omni wheel which is a special wheel
4 categories that can move both laterally and transversally allows for
 Pendulum based adjustable balancers [6, 27-32]
 Path adjusting balancers [13]

3 CVT stands for Continuously Variable Transmission
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