A New Variable Stiffness Design:
Matching Requirements of the Next Robot Generation
Sebastian Wolf and Gerd Hirzinger
DLR - German Aerospace Center
Institute of Robotics and Mechatronics
D-82234 Wessling, Germany
{sebastian.wolf, gerd.hirzinger}@dlr.de
Abstract— Facing new tasks, the conventional rigid design of
robotic joints has come to its limits. Operating in unknown
environments current robots are prone to failure when hitting
unforeseen rigid obstacles. Moreover, safety constraints are a
major aspect for robots interacting with humans. In order
to operate safely, existing robotic systems in this field are
slow and have a lack of performance. To circumvent these
limitations, a new robot joint with a variable stiffness approach
(VS-Joint) is presented. It combines a compact and highly
integrated design with high performance actuation. The VS-
Joint features a highly dynamic stiffness adjustment along with
a mechanically programmable system behavior. This allows an
easy adaption to a big variety of tasks. A benefit of the joint
is its intrinsic robustness against impacts and hard contacts,
which permits faster trajectories and handling. Thus, it provides
excellent attributes for the use in shoulder and elbow joints of
an anthropomorphic robot arm.
I. INTRODUCTION
In the current robotics research a main field is focused
on the development of joints with variable mechanical
impedance, see Fig. 1, [1]–[10]. The ambition of this devel-
opment is to bring the robots closer to the human and even
in direct contact for hand to hand interaction. The robots
are to leave their separated space and assist the humans,
maybe even at their home. Therefore, the robots have to be
more gentle to their environment, but also have to be strong
enough to fulfill their purpose. Since humans designed their
surroundings for their own ergonomics, robots have to have
similar abilities for a skilled and useful assistance.
There are several reasons for building a robot with me-
chanically compliant joints like in [2]. Up to now the main
reason to deliberately introduce joint compliance was to
ensure safety to the human user. However, in [11] it is stated
that decreasing joint stiffness is an adequate countermeasure
to reduce joint torques during rigid and fast impacts with
hard surfaces and therefore protecting the robot as well. The
bandwidth of the compliance, which can be achieved by
control with rigid joints, is limited because of the time delay
in the sensor data acquisition, the control loop, and the motor
inertia [8]. Hard impacts result in high contact forces and
torques at a very small position difference between motor
This work has been partially funded by the European Commission’s Sixth
Framework Programme as part of the projects SMERobot
TM
under grant
no. 011838 and PHRIENDS under grant no. 045359.
Fig. 1. Design study of DLR’s integrated Hand-Arm-System
and link. The reaction time of the robot limits the speed
of the trajectory to ensure that the force and torque limits
are not exceeded. Lower stiffness in the joint provides a
longer time span to react to the impact and to avoid an
external overload. The balancing of the external torque by the
mechanical compliance allows to move on faster trajectories
without exceeding the safety limits but has a loss in the
system accuracy.
Besides of the safety aspect, a flexible joint has an
advantage in the system performance compared to a stiff
joint. The flexibility itself can be seen as a mechanical
energy storage, or capacitor. It can be used for buffering
external or motor torque, and if the additional inertia is
kept small, the bandwidth of the compliance is almost the
same as the one of the decoupled system. With adequately
planed trajectories the stored energy can be added where
required t o the mechanical energy supplied by the joint
motor. This enables the link to be accelerated to a much
higher peak velocity than the maximum joint motor speed
and thus enhances the joint performance significantly.
Introducing a possibility to change the stiffness of the joint
while the robot is operating permits a further enhancement
2008 IEEE International Conference on
Robotics and Automation
Pasadena, CA, USA, May 19-23, 2008
978-1-4244-1647-9/08/$25.00 ©2008 IEEE. 1741
of the skills of a joint [3]. Similar to a human, who can
change the stiffness of his joints by straining the agonist
and the antagonist, the stiffness can be changed according to
the performed task. One approach for a variable stiffness is
an antagonistic system like in the natural archetype, which
is successfully implemented in [4], [5], [6]. Two opposing
actuators of similar size and series elastic elements drive one
link by moving in the same direction and change the joint
stiffness by moving in the opposite direction. In every case
the friction of both motors and maybe the spring mechanisms
determine an energy loss. Furthermore, unless less efficient
non-backdrivable gears are used, a high stiffness setting
demands a constant torque of both actuators in opposing
directions. This has also some drawbacks in the energy con-
sumption. The approach in [7] aims at a reduction of these
effects by motor cross-coupling. However, an antagonistic
system is capable to distribute the power of both motors
completely to the change of stiffness. Using a setup in which
the motors are not opposed in the antagonistical way promise
to have less energy consumption, a smaller volume and lower
mass [8], [9], [10]. This of course depends on the design
and the desired task. When the mechanical behavior of the
system can be adjusted close to the desired overall system
behavior, it is possible to reduce the control effort with
preexisting knowledge of the desired application (impedance
matching). Especially for cyclic motions and trajectories,
in which the link has to be stopped and accelerated in
the opposite direction like walking, running, or throwing,
a preset can be given to the system according to the applied
load and speed [12], [13], [14]. In some cases one stiffness
preset is enough for the whole performed application, but
in a real environment the robot has to adapt its stiffness to
changing objects and desired tasks. In this case a continuous
and fast change of the stiffness setup is needed. Compared to
a conventional robot like the DLR Justin [15], the stiffness of
a variable stiffness joint is still orders of magnitude less. In an
unknown environment with the possibility of sudden impacts,
the joint will be set to a stiff setup to prevent the joint from
overload and running into the hardware limits. High stiffness
will provide better results in a precise positioning task. In
contrary a soft preset will be the best choice for a gentle
manipulation in a sensitive environment.
The previous considerations are leading to the develop-
ment of the variable stiffness joint (VS-Joint) presented in
the following sections. Compared to state-of-the-art systems
the new development addresses particularly the performance,
compactness, and friction of the system.
II. VS-JOINT MECHANICS
A. Requirements
The aim of the development of the new VS-Joint (patent
pending) is to introduce a mechanical passive compliance
into a robot joint. It should be possible to change the stiffness
of the joint continuously and with the maximum load applied.
The maximum output torque should be at least 120 Nm.
Other design goals are low weight, and a compact and robust
mechanics, which allows the assembly in a robot arm system
Harmonic Drive Gear
Circular Spline
Flex Spline
Wave Generator
Variable Stiffness
Mechanism
Fig. 2. Principle of variable stiffness joint mechanics. The circular spline
of the harmonic drive gear is supported by the new mechanism.
of the size of a human arm. Low friction and inertia at the
link side are required for a high bandwidth of the spring
mechanism and a low energy loss in operation.
B. Design
The concept of the VS-Joint is based on two motors of
different size t o change the link position and the stiffness
preset separately, see Fig. 2. The high power motor changes
the link position and is connected to the link via a harmonic
drive gear. Mechanical compliance is introduced by the VS-
Joint mechanism, which forms a flexible rotational support
between the harmonic drive gear and the joint base. The
joint stiffness is changed by a much smaller and lighter
motor, which changes the characteristic of the supporting
mechanism.
The harmonic drive gear consists of three main parts. In a
standard setup the wave generator (WG) is connected to the
motor axle, the flex spline (FS) is attached to the link and the
circular spline (CS) is fixed to the base of the joint. In the
VS-Joint the circular spline is pivoted. The mechanism of the
VS-Joint acts as a spring like support between the circular
spline and the joint base. In case of a passive compliant
deflection ϕ of the joint, the CS and the FS rotate relative
to the base. The formula for the gear motion with a nominal
transmission ratio of 100/1 is given in (1), where the angle
indices are the corresponding gear part names.
ϑ
CS
=
100
101
ϑ
FS
+
1
101
ϑ
WG
(1)
The VS-Joint mechanism provides a centering torque τ
against the compliant joint deflection. The extent of the
torque can be influenced by the stiffness actuator. The
mechanism transforms the rotation of the CS into a linear
motion of a slider, see Fig. 3. This is done by 4 cam rollers
running on a rotationally symmetric cam disk, which is
connected to the CS. The cam rollers are connected to the
slider, which is guided by linear bearings in axial direction.
A motion of the slider compresses 4 spir al springs, which
results in a force on the cam rollers, see Fig. 4. The force is
transmitted by the cam rollers to the cam disk and results in
a centering torque. The force of the springs can be increased
by moving the spring base towards the cam disk. The spring
base is realized in the form of a second slider. Preload
is created by moving the spri ng base slider via a spindle
1742
Cam Disk
(Fixed to
Circular Spline)
Cam Rollers
Connection to
Linear Bearing
Roller Slider
Spring Base Slider
Spindle
Axis of Rotation
Stiffer
Preset
Translational
Deflection
Joint
Deflection
Fig. 3. VS-Joint mechanism. The joint axis is in the vertical direction.
The cam disk rotates on a compliant joint deflection according to (1) which
results in a vertical displacement of the roller slider. A stiffer joint preset
is achieved by moving the spring base downward.
(a)
Cam Disk
Linear Bearing
Roller
(b)
Roller Position
of Undeflected Joint
α
Deflection
F
τ
Fig. 4. Unwinded schematic of the VS-Joint principle in centered (a)
and deflected (b) position. A deflection of the joint results in a horizontal
movement of the cam disk and a vertical displacement of the roller. The
spring force generates a centering torque on the cam disk
attached to the stiffness adjusting motor (Maxxon EC22 with
an intermediary planetary gear).
Concerning passive spring deflection and active joint
movement, the location of the VS-Mechanism has signifi-
cant benefits regarding the system inertia and the resulting
bandwidth. The main parts of the mechanism are rotationally
fixed to the joint base. A passive deflection rotates only the
CS, the cam disk, and i ts bearing together with the link.
The added inertia of these three parts is kept very low (see
Table I) and the joint motor with the WG are not moved. The
torque of an active joint movement is transferred directly via
the gear from the joint motor to the link without additional
friction and inertia of the VS-Mechanics.
The cam disk can have different kind of shapes. A concave
shape results in a progressive, a convex in a degressive, and a
linear in a linear system behavior. By shaping the cam disk
in a concave way with a radius lower or the same as the
TABLE I
VS-JOINT PROPERTIES
Max. Torque 160 Nm
Max. Deflection ± 14
◦
Diameter 97 mm
Length 106 mm
Weight (incl. stiffness adjuster) 1.4 kg
Link Side Inertia 2.34 × 10
−4
kg m
2
cam rollers, the system torque behavior at this point will be
a jump or a resting point respectively. It can be overcome
by a torque rising above a certain threshold. The shape of
the cam disk can also be designed to have a different system
behavior depending on the deflection direction.
C. Layout
Several cam disks have been built, however, in the fol-
lowing only one cam disk with a symmetric concave shape
of a constant radius R = 19 mm will be discussed. The
cam rollers have a radius r = 8 mm and roll on a radius
c = 33 mm relative to the joint axis. The springs have a
overall spring constant of k = 908 N/mm. The st iffness
adjusting motor position σ is limited to σ
max
= 630
◦
, which
will be considered as 100 % in the following.
In the unwinded model of the system the joint deflection
is c ϕ and the angle α is:
α = sin
−1
c ϕ
R − r
(2)
The displacement of the cam rollers y in the direction of the
joint axis
y = (R − r) (1 − cos α) (3)
and the displacement of the stiffness adjusting slider r esult
in the compression of the springs. By multiplying t his
displacement with the spring constant the spring force results
F = k
(R − r) (1 − cos α) +
σ
π
. (4)
It generates the centering torque
τ = F c tan α = kc tan α
(R − r) (1 − cos α) +
σ
π
(5)
of the system. The stiffness is
S =
dτ
dϕ
= kc
2
"
− 1 +
R − r +
σ
π
(R − r) cos α
+
+
R − r +
σ
π
c
2
ϕ
2
((R − r) cos α)
3
#
(6)
and the potential energy stored in the system is
E =
Z
ϕ
0
τdϕ = −k
1
2
c
2
ϕ
2
+
+ (R − r)
1 +
σ
π
cos α +
σ
π
− R + r
. (7)
The progressive shape of the cam disk forms an intrinsic
protection of the system, which prevents the joint from
running into the hardware limits. When they are reached, the
spring mechanism is bypassed with a mechanical blocking.
In this case the gear is the direct connection between the link
and the motor inertia. A speed difference of motor and link
then results in a torque peak, whose magnitude is depending
on the gear flexibility. This torque peak of the inner system
impact may cause serious damage to the system.
The system behavior with a deflection in positive direction
is presented in Fig. 5. The system is built symmetrically
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0 2 4 6 8 10 12 14
0
50
100
150
200
VS-Joint Torque
Deflection (deg)
Torque (Nm)
σ = 0
σ = 1/3 ∗ σ
max
σ = 2/3 ∗ σ
max
σ = σ
max
0 2 4 6 8 10 12 14
0
10
20
30
40
50
60
VS-Joint Stiffness
Deflection (deg)
Stiffness (Nm/deg)
σ = 0
σ = 1/3 ∗ σ
max
σ = 2/3 ∗ σ
max
σ = σ
max
Fig. 5. System behavior concerning the joint torque and the joint stiffness.
0 2 4 6 8 10 12 14
0
5
10
15
VS-Joint Potential Energy
Deflection (deg)
Energy (J)
σ = 0
σ = 1/3 ∗ σ
max
σ = 2/3 ∗ σ
max
σ = σ
max
0 2 4 6 8 10 12 14
0
10
20
30
40
Ratio of Max./Min. Stiffness
Deflection (deg)
Ratio
Fig. 6. Stored energy in the system and the ratio of maximum to minimum
stiffness with respect to the deflection.
and has maximum deflection of 14
◦
in both directions. In
contrast to antagonistic joints, the deflection range is not
reduced by a higher stiffness preset. On a given deflection the
stiffness of the joint and its derivative are under any condition
higher with an increased stiffness adjuster position. The
stiffness adjuster is able to change the preset continuously
between minimum and maximum, and the power of the
actuator enables the joint to change the preset bidirectionally
under full load. The ratio of maximum to minimum stiffness
is given in Fig. 6 and tends to infinity at zero deflection.
III. TESTING SETUP
The test bed (Fig. 7) consists of a motor / gear driving unit
at the base side and a hollow shaft axle with a lever at the
link side. The driving unit with a maximum output torque of
160 Nm consists of a DLR ILM 70 motor attached through
the hollow shaft link axle to a Harmonic Drive HFUS 20
(100/1). The CS of the Gear is mounted to the VS-Joint and
the FS to the link axle. A DLR magnetoresistive (MR) sensor
with a resolution of 30720 inc/rev is connected to the motor
and a Heidenhain ERN120 with a resolution of 20000 inc/rev
is attached to the link. A DLR torque sensor with a maximum
VS-Joint
Joint Motor
Link Encoder
Torque Sensor
Load
Fig. 7. Testing setup equipped with 7.0 kg load.
sensor range of ± 200 Nm is mounted at the lever base. The
sensor data acquisition is done by a National Instruments
NI6602 and a NI6025E card. The motor controllers are two
Sensodrive Unireg12 connected via CAN-Bus to a Softing
CAN-AC2 card. The testbed is controlled by a computer with
a QNX Software Systems real time operating system QNX
R
Neutrino
R
. The control of the two motors is done position
based with PD controllers.
The lever can be equipped with loads up to 7.0 kg.
Depending on the loads the link inertia varies between
0.124 kg m
2
and 2.133 kg m
2
. In the further tests the upright
position of the lever is defined as the zero position and
the positive displacement is in the mathematical positive
direction seen from the joint motor side.
IV. TESTS & DEMONSTRATIONS
A. Evaluation
The evaluation of the torque model, which is based on (5),
was done with a fixed link at the end of the lever. In that setup
the calculated torque is evaluated with the torque sensor.
The theoretical torque does not include the strain of the
joint structure. The spring base slider, the spindle connected
to it, and the linear bearings do have notable flexibility,
which can not be neglected. The strain was identified to be
linear to the applied torque and results in a factor of 0.78
to the calculated torque. Fig. 8 shows the estimated torque
including the correction factor plotted against the sensor data.
The test trajectory of the joint motor is a position ramp, in
which the joint is moving with a constant velocity between
the joint deflection limit s. This is done with minimum and
maximum stiffness preset. The plot shows a very good linear
correlation with a small hysteresis, which is the result of
friction and sensor hysteresis.
A crucial factor to the system performance is the change
of the stiffness preset. The time to change the stiffness is
1744
−150 −100 −50 0 50 100 150
−150
−100
−50
0
50
100
150
Evaluation of Torque Estimation
Torque Sensor (Nm)
Torque Calculated (Nm)
σ = 0
σ = σ
max
Fig. 8. Estimated Torque with respect to measured torque of the sensor.
0 0.1 0.2 0.3 0.4 0.5
0
10
20
30
40
50
60
70
80
90
100
Stiffness Actuator Step Response
Time (s)
Position (%)
σ desired
σ at 0
◦
link deflection
σ at 14
◦
link deflection
Fig. 9. Step response of the stiffness actuator from minimum to maximum
with a fixed joint end at 0
◦
and 14
◦
joint deflection
decisive for the tasks and control of the system. In order
to increase the stiffness preset the stiffness actuator has to
compress the springs by moving the spring base slider. An
external load also results in a compression of the springs so
that the force applied to the spring base slider is increased.
According to this the critical movement is an increase with
external load applied. A step response with a fixed joint is
given in Fig. 9. The steady state error in the test run with
maximum joint deflection is a result of the PD controller,
which is currently used for the stiffness adjuster motor.
B. Throwing
The application of throwing a ball is a good example to
show the performance enhancement gained by the VS-joint
in terms of maximum link velocity. For throwing a ball as far
as possible it has to be accelerated to the maximum velocity
and released at an angle of 45
◦
. The link velocity of a stiff
joint corresponds to the velocity of the driving motor. In a
flexible joint the potential energy stored in the system can
be used to accelerate the link relative to the driving motor.
Additional energy can be inserted by the stiffness adjuster of
the variable stiffness joint to gain the fastest possible motion.
A lacrosse stick head was mounted to the top of the link
lever for the throwing tests, see Fig. 10 and the accompany-
ing video. The ball is a 64 g rubber ball for school lacrosse.
The distance l between the link axis and the center of the
Fig. 10. Throwing setup with a lacrosse stick head mounted to the top of
the lever.
0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5
−70
−60
−50
−40
−30
−20
Throwing Trajectory
Time (s)
Position (deg)
Desired Motor Position
Motor Position
Link Position
0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5
50
60
70
80
90
100
Stiffness Actuator Position
Time (s)
Position (%)
0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5
−400
−200
0
200
400
600
Throwing Velocity
Time (s)
Velocity (deg/s)
Motor Velocity
Link Velocity
Fig. 11. A strike out trajectory of the joint motor in combination with an
increase of the stiffness preset are used to gain maximum link velocity.
ball when the ball leaves the lever is approximately 0.78 m.
A simple strike out trajectory is used for the demonstration
in order to gain a high link velocity (Fig. 11). A joint motor
position ramp accelerates the link in the negative direction
to add kinetic energy to the link. When the motor stops
and reverts, this energy is transformed into potential energy
stored in the VS-Joint. The stiffness adjuster starts moving
to the maximum pretension, which additionally increases the
potential energy of the system. The effect can be seen in
Fig. 6. The stored energy in the system at the same joint
deflection is higher with an increased stiffness actuator po-
sition. Afterwards the joint motor accelerates in the positive
direction and adds the kinetic energy to the stored energy
in the VS-Joint. When the joint motor reaches its maximum
speed t he link is further accelerated by the potential energy.
As long as the link is accelerating, the ball can not be
faster than the link, and the shape of the lacrosse stick head
1745