The knee-locking mechanism consists of a knee A, knee plate B, locking axle C, locking hook D, base plate E, and a DC motor F as shown in Fig.. The knee-locking mechanism consists of a k
Trang 1Fig 15 Counting steps in passive walking The first landing is counted as the zeroth step and
the second landing as the first
Successful Steps Number of times (in 100 launch)
Table 3 Experimental result for each pitch angle spring constant
Fig 16 Comparison of the foot motion for varying spring stiffness
motions are coordinated From (Narukawa et al., 2009a), the value of the spring constant of
the extension spring for roll motion is determined to be 4900 N/m with a torsional spring
stiffness of about 9 N-m/rad Figure 14 shows the relationship between the ankle angle and
the torque applied by the springs for pitch motion when the spring constant is 3920, 6180,
5.1 Successful Steps at Different Spring Constants for Pitch Motion
Figure 15 shows how we count the number of realized steps After the launch in Fig 15 (a),first landing is counted as the zeroth step and second landing is the first step, as shown inFig 15 (b) and (c) When the swing leg lands and the heel is behind the toe of the stancefoot, we do not count the landing as a successful step and regard the walking as a failure, asshown in Fig 15 (e) and (f) In some situations, we do not count a landing as a successfulstep even though the swing leg lands in front of the stance leg Table 3 shows the experimen-tal results We changed pitch spring constant of the ankles and launched the biped walker
100 times for each settings The spring constant ∞ [N/m] means that we locked the anklepitch movements with wires instead of springs However, the feet are not ideal rigid bodiesbecause we attached sponge sheets to the soles of the feet The result shows that a mediumspring constant effectively stabilizes passive walking High and low spring constants are in-effective because unsuccessful trials (0 step) occurred frequently, producing a low expectation
of successful steps
5.2 Foot Motion with the Ground
The spring stiffness of the pitch motion affects the foot motion with the floor Figure 16 pares the foot motion for different spring stiffness When the spring constant is 3920 N/m,which is equal to a torsional spring stiffness of about 7 Nm/rad, the foot of the stance legremains in full contact with the floor until the heel of the swing leg touches the floor Next,the front foot fully impacts the floor and rebound occurs, as indicated in Fig 17 On the otherhand, when the torsional spring stiffness is large, e.g., the spring constant is 9320 N/m, therotation of the stance foot around the toe occurs before the swing foot touches the floor andthe rebound after the full contact of the front foot is dramatically reduced A high torsionalspring stiffness for pitch motion leads to a smooth transition at the exchange of the stance leg.When the torsional spring stiffness is very large, the pitch angle is always 0, the stance footalmost always rotates around the heel or toe, and rebound does not occur
com-6 Conclusions
This paper presents a simple 3D passive biped walker with flat feet and ankle springs mental tests were performed to investigate the effects of torsional spring stiffness on the pitch
Trang 2Experi-motion at the ankle joints of the walker When the spring stiffness is low, oscillating Experi-motion
is induced by the impact of the feet with the ground Experimental results showed that using
springs with appropriate torsional spring stiffness effectively reduces the oscillating motion
The rebound of the front foot after full contact with the ground reduces dramatically with
appropriate torsional spring stiffness Appropriate stiffness enables the biped walker to walk
smoothly and also stabilizes the walker However, when the spring stiffness is either high or
low, it become difficult for the walker to walk
ACKNOWLEDGMENTS
This work was supported in part by Grant in Aid for the Global Center of Excellence Program
for “Center for Education and Research of Symbiotic, Safe and Secure System Design" from
the Ministry of Education, Culture, Sports, Science and Technology in Japan
7 References
Adolfsson, J., Dankowicz, H., and Nordmark, A (2001) 3D passive walkers: Finding periodic
gaits in the presence of discontinuities Nonlinear Dynamics, 24(2):205–229.
Coleman, M J., Garcia, M., Mombaur, K., and Ruina, A (2001) Prediction of stable walking
for a toy that cannot stand Physical Review E, 64(2):22901–.
Coleman, M J and Ruina, A (1998) An uncontrolled walking toy that cannot stand still
Physical Review Letters, 80(16):3658–3661.
Collins, S and Ruina, A (2005) A bipedal walking robot with efficient and human-like gait
Proceedings of the 2005 IEEE International Conference on Robotics and Automation, pages
1983–1988
Collins, S., Ruina, A., Tedrake, R., and Wisse, M (2005) Efficient bipedal robots based on
passive-dynamic walkers Science, 307(5712):1082–1085.
Collins, S., Wisse, M., and Ruina, A (2001) A three-dimensional passive-dynamic walking
robot with two legs and knees International Journal of Robotics Research, 20(7):607–
615
Garcia, M (1999) Stability, scaling, and chaos in passive-dynamic gait models PhD thesis, Cornell
University
Garcia, M., Chatterjee, A., and Ruina, A (2000) Efficiency, speed, and scaling of
two-dimensional passive-dynamic walking Dynamics and Stability of Systems, 15(2):75–99.
Garcia, M., Chatterjee, A., Ruina, A., and Coleman, M (1998) The simplest walking model:
Stability, complexity, and scaling Journal of Biomechanical Engineering-Transactions of
the ASME, 120(2):281–288.
Goswami, A., Espiau, B., and Keramane, A (1996) Limit cycles and their stability in a
pas-sive bipedal gait Proceedings of the 1996 IEEE International Conference on Robotics and
Automation, pages 246–251.
Goswami, A., Thuilot, B., and Espiau, B (1998) A study of the passive gait of a
compass-like biped robot: Symmetry and chaos International Journal of Robotics Research,
17(12):1282–1301
Hobbelen, D G E and Wisse, M (2007) Limit cycle walking In Hackel, M., editor, Humanoid
Robots: Human-like Machines, pages 277–294 I-Tech Education and Publishing,
Vi-enna, Austria
Ikemata, Y., Sano, A., and Fujimoto, H (2006) A physical principle of gait generation and its
stabilization derived from mechanism of fixed point Proceedings of the 2006 Conference
on International Robotics and Automation, pages 836–841.
Kinugasa, T., Kotake, K., Haruki, T., Tanaka, H., and Yoshida, K (2008) 3D passive dynamic
walker with sprung ankle and flat foot -a design method by natural frequency
in-dex without yaw and roll compensator- Proceedings of the 2008 JSME Conference on
Robotics and Mechatronics, pages 1P1–B12–.
Kuo, A D (1999) Stabilization of lateral motion in passive dynamic walking International
Journal of Robotics Research, 18(9):917–930.
McGeer, T (1990) Passive dynamic walking International Journal of Robotics Research, 9(2):62–
82
McGeer, T (1993) Passive dynamic biped catalogue, 1991 In Chatila, R and Hirzinger, G.,
editors, Experimental Robotics II: The 2nd International Symposium, Toulouse, France, June
25-27 1991, pages 465–490 Springer-Verlag.
McMahon, T A (1984) Mechanics of locomotion International Journal of Robotics Research,
3(2):4–28
Narukawa, T., Yokoyama, K., Takahashi, M., and Yoshida, K (2008) A simple 3D
straight-legged passive walker with flat feet and ankle springs IEEE/RSJ International
Confer-ence on Intelligent Robots and Systems, pages 2952–2957.
Narukawa, T., Yokoyama, K., Takahashi, M., and Yoshida, K (2009a) Design and construction
of a simple 3D straight-legged passive walker with flat feet and ankle springs JSME
Journal of System Design and Dynamics, 3(1):1–12.
Narukawa, T., Takahashi, M., and Yoshida, K (2009b) Design and Stability Analysis of a 3D
Rimless Wheel with Flat Feet and Ankle Springs JSME Journal of System Design and
Dynamics, 3(3):258-269.
Schwab, A L and Wisse, M (2001) Basin of attraction of the simplest walking model
Pro-ceedings of the ASME Design Engineering Technical Conference, pages DETC2001/VIB–
21363–
Tedrake, R., Zhang, T W., Fong, M.-F., and Seung, H S (2004) Actuating a simple 3D
pas-sive dynamic walker Proceedings of the IEEE International Conference on Robotics and
Automation, 2004(5):4656–4661.
Tedrake, R L (2004) Applied Optimal Control for Dynamically Stable Legged Locomotion PhD
thesis, Massachusetts institute of technology
Wisse, M., Hobbelen, D G E., Rotteveel, R J J., Anderson, S O., and Zeglin, G J (2006)
Ankle springs instead of arc-shaped feet for passive dynamic walkers Proceedings of
the IEEE-RAS International Conference on Humanoid Robots, pages 110–116.
Wisse, M and Schwab, A L (2005) Skateboards, bicycles, and three-dimensional biped
walk-ing machines: Velocity-dependent stability by means of lean-to-yaw couplwalk-ing
Inter-national Journal of Robotics Research, 24(6):417–429.
Wisse, M., Schwab, A L., van der Linde, R Q., and van der Helm, F C T (2005) How to keep
from falling forward: Elementary swing leg action for passive dynamic walkers IEEE
Transactions on Robotics, 21(3):393–401.
Wisse, M., Schwab, A L., and vander Linde, R Q (2001) A 3D passive dynamic biped with
yaw and roll compensation Robotica, 19:275–284.
Wisse, M and van Frankenhuyzen, J (2003) Design and construction of mike; a 2D
au-tonomous biped based on passive dynamic walking Proceedings of the Second
In-ternational Symposium on Adaptive Motion of Animals and Machines, pages 4–8.
Trang 3motion at the ankle joints of the walker When the spring stiffness is low, oscillating motion
is induced by the impact of the feet with the ground Experimental results showed that using
springs with appropriate torsional spring stiffness effectively reduces the oscillating motion
The rebound of the front foot after full contact with the ground reduces dramatically with
appropriate torsional spring stiffness Appropriate stiffness enables the biped walker to walk
smoothly and also stabilizes the walker However, when the spring stiffness is either high or
low, it become difficult for the walker to walk
ACKNOWLEDGMENTS
This work was supported in part by Grant in Aid for the Global Center of Excellence Program
for “Center for Education and Research of Symbiotic, Safe and Secure System Design" from
the Ministry of Education, Culture, Sports, Science and Technology in Japan
7 References
Adolfsson, J., Dankowicz, H., and Nordmark, A (2001) 3D passive walkers: Finding periodic
gaits in the presence of discontinuities Nonlinear Dynamics, 24(2):205–229.
Coleman, M J., Garcia, M., Mombaur, K., and Ruina, A (2001) Prediction of stable walking
for a toy that cannot stand Physical Review E, 64(2):22901–.
Coleman, M J and Ruina, A (1998) An uncontrolled walking toy that cannot stand still
Physical Review Letters, 80(16):3658–3661.
Collins, S and Ruina, A (2005) A bipedal walking robot with efficient and human-like gait
Proceedings of the 2005 IEEE International Conference on Robotics and Automation, pages
1983–1988
Collins, S., Ruina, A., Tedrake, R., and Wisse, M (2005) Efficient bipedal robots based on
passive-dynamic walkers Science, 307(5712):1082–1085.
Collins, S., Wisse, M., and Ruina, A (2001) A three-dimensional passive-dynamic walking
robot with two legs and knees International Journal of Robotics Research, 20(7):607–
615
Garcia, M (1999) Stability, scaling, and chaos in passive-dynamic gait models PhD thesis, Cornell
University
Garcia, M., Chatterjee, A., and Ruina, A (2000) Efficiency, speed, and scaling of
two-dimensional passive-dynamic walking Dynamics and Stability of Systems, 15(2):75–99.
Garcia, M., Chatterjee, A., Ruina, A., and Coleman, M (1998) The simplest walking model:
Stability, complexity, and scaling Journal of Biomechanical Engineering-Transactions of
the ASME, 120(2):281–288.
Goswami, A., Espiau, B., and Keramane, A (1996) Limit cycles and their stability in a
pas-sive bipedal gait Proceedings of the 1996 IEEE International Conference on Robotics and
Automation, pages 246–251.
Goswami, A., Thuilot, B., and Espiau, B (1998) A study of the passive gait of a
compass-like biped robot: Symmetry and chaos International Journal of Robotics Research,
17(12):1282–1301
Hobbelen, D G E and Wisse, M (2007) Limit cycle walking In Hackel, M., editor, Humanoid
Robots: Human-like Machines, pages 277–294 I-Tech Education and Publishing,
Vi-enna, Austria
Ikemata, Y., Sano, A., and Fujimoto, H (2006) A physical principle of gait generation and its
stabilization derived from mechanism of fixed point Proceedings of the 2006 Conference
on International Robotics and Automation, pages 836–841.
Kinugasa, T., Kotake, K., Haruki, T., Tanaka, H., and Yoshida, K (2008) 3D passive dynamic
walker with sprung ankle and flat foot -a design method by natural frequency
in-dex without yaw and roll compensator- Proceedings of the 2008 JSME Conference on
Robotics and Mechatronics, pages 1P1–B12–.
Kuo, A D (1999) Stabilization of lateral motion in passive dynamic walking International
Journal of Robotics Research, 18(9):917–930.
McGeer, T (1990) Passive dynamic walking International Journal of Robotics Research, 9(2):62–
82
McGeer, T (1993) Passive dynamic biped catalogue, 1991 In Chatila, R and Hirzinger, G.,
editors, Experimental Robotics II: The 2nd International Symposium, Toulouse, France, June
25-27 1991, pages 465–490 Springer-Verlag.
McMahon, T A (1984) Mechanics of locomotion International Journal of Robotics Research,
3(2):4–28
Narukawa, T., Yokoyama, K., Takahashi, M., and Yoshida, K (2008) A simple 3D
straight-legged passive walker with flat feet and ankle springs IEEE/RSJ International
Confer-ence on Intelligent Robots and Systems, pages 2952–2957.
Narukawa, T., Yokoyama, K., Takahashi, M., and Yoshida, K (2009a) Design and construction
of a simple 3D straight-legged passive walker with flat feet and ankle springs JSME
Journal of System Design and Dynamics, 3(1):1–12.
Narukawa, T., Takahashi, M., and Yoshida, K (2009b) Design and Stability Analysis of a 3D
Rimless Wheel with Flat Feet and Ankle Springs JSME Journal of System Design and
Dynamics, 3(3):258-269.
Schwab, A L and Wisse, M (2001) Basin of attraction of the simplest walking model
Pro-ceedings of the ASME Design Engineering Technical Conference, pages DETC2001/VIB–
21363–
Tedrake, R., Zhang, T W., Fong, M.-F., and Seung, H S (2004) Actuating a simple 3D
pas-sive dynamic walker Proceedings of the IEEE International Conference on Robotics and
Automation, 2004(5):4656–4661.
Tedrake, R L (2004) Applied Optimal Control for Dynamically Stable Legged Locomotion PhD
thesis, Massachusetts institute of technology
Wisse, M., Hobbelen, D G E., Rotteveel, R J J., Anderson, S O., and Zeglin, G J (2006)
Ankle springs instead of arc-shaped feet for passive dynamic walkers Proceedings of
the IEEE-RAS International Conference on Humanoid Robots, pages 110–116.
Wisse, M and Schwab, A L (2005) Skateboards, bicycles, and three-dimensional biped
walk-ing machines: Velocity-dependent stability by means of lean-to-yaw couplwalk-ing
Inter-national Journal of Robotics Research, 24(6):417–429.
Wisse, M., Schwab, A L., van der Linde, R Q., and van der Helm, F C T (2005) How to keep
from falling forward: Elementary swing leg action for passive dynamic walkers IEEE
Transactions on Robotics, 21(3):393–401.
Wisse, M., Schwab, A L., and vander Linde, R Q (2001) A 3D passive dynamic biped with
yaw and roll compensation Robotica, 19:275–284.
Wisse, M and van Frankenhuyzen, J (2003) Design and construction of mike; a 2D
au-tonomous biped based on passive dynamic walking Proceedings of the Second
In-ternational Symposium on Adaptive Motion of Animals and Machines, pages 4–8.
Trang 5In this chapter we will present the design and development of two knee mechanisms One
uses permanent magnets to lock the knee in its extended position and the other features an
active mechanism for releasing the passively locked knee We will also present a comparison
between the experimental results achieved with each of the two knee mechanisms
One of the big, and still unsolved, problems in robotics is achieving efficient and stable
bipedal walking There are two main strategies used to control walking First, the traditional
approach is to control the joint-angle of every joint at all times Crucial disadvantages of this
approach are that it results in a non-efficient gait in terms of energy consumption (Collins et
al., 2005), it requires complex controllers and programming, and this strategy often results in
gaits that are unnatural when compared to the human gait Second is a somewhat new
strategy called passive-dynamic walking, introduced by Tad McGeer (McGeer 1990) in the
late 80’s, early 90’s A walker based on the passive-dynamic walking principle uses its own
mechanical dynamics properties to determine its movement Such walkers can walk down
slight inclines without any actuators, sensors or controllers The energy that is necessary in
order to sustain the walking motion is provided by gravity The force of gravity is also
enough to offset the losses due to the impact of the feet on the ground and friction The
advantages of passive-dynamic walking are high-energy efficiency, simple or no control,
and a human-like gait The main disadvantage is that because they are not actively powered,
they can only walk on downhill slopes This disadvantage can be eliminated by modifying
walkers to include actuators that supply the necessary power instead of gravity (Collins and
Ruina, 2005; Wisse and Frankenhuyzen, 2003; Wisse, 2004) This enables them to walk not
only downhill, but on level and uphill surfaces as well This possibility greatly increases the
prospects for practical application
The knee mechanism is a major part in passive-dynamic walkers There are several different
designs that have been implemented in walkers up to now The original walker built by
McGeer uses a mechanism with suction cups that keeps the knee extended as shown in
Figure 1 The drawback of the suction cups design is that it is difficult to set up and not very
efficient
9
Trang 6Fig 1 Knee design with suction cups knee-locking
Another popular design is used in the University of Delft’s Mike (Wisse and
Frankenhuyzen, 2003) and subsequent walkers Max and Denise (Wisse, 2004) The locking
of the knee is achieved actively by McKibben muscles, which are counteracted by weak
springs as shown in Fig.2 As a drawback we can mention that the McKibben muscles are
not linear, and require controller that takes this feature into account They also require a
source of air
Fig 2 Knee design with McKibben muscles knee-locking
A third popular knee design is implemented in the Cornell powered biped (3) It features an electromagnetic release system shown in Fig.3, where (A), (B), (C), (D), (E), (F), (G) and (H) are a latch arm, a roller, a shank, a hinge, a shaft, a latch surface, a thigh and a solenoid, respectively This design is robust and easy to control, but it is comprised of many parts, which makes it quite complicated A similar design, where an electromagnetic clutch is used
to engage or disengage a knee motor is developed by Baines (Baines, 2005)
Fig 3 Knee design with electromagnetic knee-release
We developed our two knee locking mechanism with simplicity in mind We wanted to understand if it was possible to develop a passive walker and a knee mechanism specifically based only on observation and experimentation without any modeling and simulations A detailed model describing the mechanisms of generation and stabilization of a fixed point of passive walking, as well as leg-swing motion analysis of a passive-dynamic walker can be found in the research done by Prof Sano’s team at the Nagoya Institute of Technology (Ikemata et al., 2007), (Ikemata et al., 2008) Our aim was to build a mechanism that is simple, robust, and easy to use and set up The purposes of this chapter are to present the mechanical design of the two knee mechanisms, to introduce the achieved experimental results, to make a comparison between them, and to discuss their effectiveness
2 Knee Mechanism with Permanent Magnets
The dynamics of passive-dynamic walkers cause the swinging leg to bend and extend on its own However, in order to achieve a stable gait, the knee must be able to swing with minimal friction, meaning minimal energy loss Taking this into consideration, the most logical choice for the knee joint is a ball bearing Additionally, the knee must be equipped with a knee-locking mechanism that supports the knee during its extended phase and prevents it from bending while bearing the weight of the walker
For our walker, the knee is cut from an aluminum block and is comprised of only an upper knee, to which the aluminum lower leg is attached directly through a shaft and a pair of ball
Trang 7Fig 1 Knee design with suction cups knee-locking
Another popular design is used in the University of Delft’s Mike (Wisse and
Frankenhuyzen, 2003) and subsequent walkers Max and Denise (Wisse, 2004) The locking
of the knee is achieved actively by McKibben muscles, which are counteracted by weak
springs as shown in Fig.2 As a drawback we can mention that the McKibben muscles are
not linear, and require controller that takes this feature into account They also require a
source of air
Fig 2 Knee design with McKibben muscles knee-locking
A third popular knee design is implemented in the Cornell powered biped (3) It features an electromagnetic release system shown in Fig.3, where (A), (B), (C), (D), (E), (F), (G) and (H) are a latch arm, a roller, a shank, a hinge, a shaft, a latch surface, a thigh and a solenoid, respectively This design is robust and easy to control, but it is comprised of many parts, which makes it quite complicated A similar design, where an electromagnetic clutch is used
to engage or disengage a knee motor is developed by Baines (Baines, 2005)
Fig 3 Knee design with electromagnetic knee-release
We developed our two knee locking mechanism with simplicity in mind We wanted to understand if it was possible to develop a passive walker and a knee mechanism specifically based only on observation and experimentation without any modeling and simulations A detailed model describing the mechanisms of generation and stabilization of a fixed point of passive walking, as well as leg-swing motion analysis of a passive-dynamic walker can be found in the research done by Prof Sano’s team at the Nagoya Institute of Technology (Ikemata et al., 2007), (Ikemata et al., 2008) Our aim was to build a mechanism that is simple, robust, and easy to use and set up The purposes of this chapter are to present the mechanical design of the two knee mechanisms, to introduce the achieved experimental results, to make a comparison between them, and to discuss their effectiveness
2 Knee Mechanism with Permanent Magnets
The dynamics of passive-dynamic walkers cause the swinging leg to bend and extend on its own However, in order to achieve a stable gait, the knee must be able to swing with minimal friction, meaning minimal energy loss Taking this into consideration, the most logical choice for the knee joint is a ball bearing Additionally, the knee must be equipped with a knee-locking mechanism that supports the knee during its extended phase and prevents it from bending while bearing the weight of the walker
For our walker, the knee is cut from an aluminum block and is comprised of only an upper knee, to which the aluminum lower leg is attached directly through a shaft and a pair of ball
Trang 8bearings (Trifonov and Hashimoto, 2006) For the locking mechanism, we are using a knee
plate spacer and a knee plate, cut from acrylic, as with the original McGeer design, but we
decided to try a new approach by using magnets instead of a suction cup We adjust the
locking magnetic force by changing the distance between the magnet(s) and the steel plate
This can be achieved either by using magnets with different sizes or by using a different
number of magnets The smaller the distance is, the stronger the force Another advantage of
the magnetic lock is that it does not require physical contact between the locking parts
(magnet and steel plate) In this way the material wear is reduced and the lock can be used
longer without having to worry about replacing some of its parts 3D renderings are shown
in Fig 4, where (A) is knee, (B) is knee plate, (C) is magnet(s), and (D) is a steel plate A
drawing of the knee mechanism with some main dimensions is shown in Fig 5
Fig 4 3D renderings of the knee mechanism with permanent magnets
Fig 5 Drawing of the knee mechanism with permanent magnets
3 Knee Mechanism with an Active Release System
We designed a second newer, simpler, and lower in weight knee-locking mechanism (Trifonov and Hashimoto, 2007) The locking mechanism is constructed of acrylic, ABS, steel, and aluminum The knee-locking mechanism consists of a knee (A), knee plate (B), locking axle (C), locking hook (D), base plate (E), and a DC motor (F) as shown in Fig 6 and Fig 7 Additionally, there is a switch attached to each foot of the walker, which is used to control the DC motor, but is not shown in the figure The entire knee mechanism was designed in 3D modeling software and cut on a CAM machine The knee is cut from aluminum, the knee plate from acrylic, the locking axle from steel, and the locking hook and the base plate are cut from ABS
An active release system has been implemented before on a passive-dynamic walker The Cornell powered biped (Collins and Ruina, 2005) uses an electromagnetic solenoid for the release of the passively locked knee mechanism The advantages of our system are the much simpler design and the absence of a controller
The locking action is done passively As the swing leg extends before hitting the ground, the locking axle hits the front edge of the locking hook, lifting it After the locking axle passes under the hook, it comes back down to lock the axle, effectively locking the knee itself The locking hook is balanced by a counter weight in such a way that it comes back down to its initial position after the locking axle has lifted it Just before the stance leg lifts from the ground and starts to swing, the foot switch comes into contact with the ground and switches
to the ON position, thus turning on the power for the DC motor This causes the motor to lift the locking hook and release the knee Immediately after the leg lifts off the ground and starts swinging, the foot switch returns to the OFF position, cutting the power, and the locking hook returns to its initial position The foot switch is mounted to the side of the foot plate, such that it does not influence the walking of the machine
Fig 6 3D renderings of the knee mechanism with an active release
Trang 9bearings (Trifonov and Hashimoto, 2006) For the locking mechanism, we are using a knee
plate spacer and a knee plate, cut from acrylic, as with the original McGeer design, but we
decided to try a new approach by using magnets instead of a suction cup We adjust the
locking magnetic force by changing the distance between the magnet(s) and the steel plate
This can be achieved either by using magnets with different sizes or by using a different
number of magnets The smaller the distance is, the stronger the force Another advantage of
the magnetic lock is that it does not require physical contact between the locking parts
(magnet and steel plate) In this way the material wear is reduced and the lock can be used
longer without having to worry about replacing some of its parts 3D renderings are shown
in Fig 4, where (A) is knee, (B) is knee plate, (C) is magnet(s), and (D) is a steel plate A
drawing of the knee mechanism with some main dimensions is shown in Fig 5
Fig 4 3D renderings of the knee mechanism with permanent magnets
Fig 5 Drawing of the knee mechanism with permanent magnets
3 Knee Mechanism with an Active Release System
We designed a second newer, simpler, and lower in weight knee-locking mechanism (Trifonov and Hashimoto, 2007) The locking mechanism is constructed of acrylic, ABS, steel, and aluminum The knee-locking mechanism consists of a knee (A), knee plate (B), locking axle (C), locking hook (D), base plate (E), and a DC motor (F) as shown in Fig 6 and Fig 7 Additionally, there is a switch attached to each foot of the walker, which is used to control the DC motor, but is not shown in the figure The entire knee mechanism was designed in 3D modeling software and cut on a CAM machine The knee is cut from aluminum, the knee plate from acrylic, the locking axle from steel, and the locking hook and the base plate are cut from ABS
An active release system has been implemented before on a passive-dynamic walker The Cornell powered biped (Collins and Ruina, 2005) uses an electromagnetic solenoid for the release of the passively locked knee mechanism The advantages of our system are the much simpler design and the absence of a controller
The locking action is done passively As the swing leg extends before hitting the ground, the locking axle hits the front edge of the locking hook, lifting it After the locking axle passes under the hook, it comes back down to lock the axle, effectively locking the knee itself The locking hook is balanced by a counter weight in such a way that it comes back down to its initial position after the locking axle has lifted it Just before the stance leg lifts from the ground and starts to swing, the foot switch comes into contact with the ground and switches
to the ON position, thus turning on the power for the DC motor This causes the motor to lift the locking hook and release the knee Immediately after the leg lifts off the ground and starts swinging, the foot switch returns to the OFF position, cutting the power, and the locking hook returns to its initial position The foot switch is mounted to the side of the foot plate, such that it does not influence the walking of the machine
Fig 6 3D renderings of the knee mechanism with an active release
Trang 10Fig 7 Drawing of the knee mechanism with an active release
4 Experiments and Results
To compare the two knee mechanisms, experiments were conducted with the same walker
shown in Fig 8, built from square aluminum tubes for the legs and 2mm thick steel plate for
the feet (Trifonov and Hashimoto, 2006) For the thighs and lower legs, we used 2.5 by 2.5cm
square aluminum tubes with lengths of 34 and 43.5cm respectively The total height of the
walker is 89cm and the radius of the feet is 12.3cm The total weight is 4.5kg The knees were
outfitted first with the magnetic system and then with the active release one The walker
was set on a ramp, which measures 3m in length, 90cm in width, and has a 3 grade relative
to the ground The ramp is covered with a rubber mat to reduce the chance of foot slippage
We performed several sets of a hundred trials (walks) down the ramp for both knee
mechanisms and counted the steps that the walker completed each time We denote a trial
as successful if the walker manages to make five to seven steps before it exits the ramp
While five to seven steps may seem short, we postulate that after five steps, the walker has
achieved a steady gait, and would ideally continue assuming a longer ramp existed
However, the impracticality of a longer ramp led us to set this number of steps as the
criteria for deciding walk success Fig 9 shows a comparison between the two knee
mechanism designs in terms of average number of steps made in each of the hundred trials
As the results show, using the knee mechanism with active release, we can achieve a
reasonable amount of successful trials Out of a hundred trials, the walker achieved an
average of forty-four successful walks with the active release system, while the magnetic
approach resulted in only seven In addition, using the active mechanism produces fewer
failures than the magnetic one
Fig 8 Walker on the ramp, outfitted with knees with active release system
Fig 9 Comparison between the experimental results achieved with the two mechanisms
Trang 11Fig 7 Drawing of the knee mechanism with an active release
4 Experiments and Results
To compare the two knee mechanisms, experiments were conducted with the same walker
shown in Fig 8, built from square aluminum tubes for the legs and 2mm thick steel plate for
the feet (Trifonov and Hashimoto, 2006) For the thighs and lower legs, we used 2.5 by 2.5cm
square aluminum tubes with lengths of 34 and 43.5cm respectively The total height of the
walker is 89cm and the radius of the feet is 12.3cm The total weight is 4.5kg The knees were
outfitted first with the magnetic system and then with the active release one The walker
was set on a ramp, which measures 3m in length, 90cm in width, and has a 3 grade relative
to the ground The ramp is covered with a rubber mat to reduce the chance of foot slippage
We performed several sets of a hundred trials (walks) down the ramp for both knee
mechanisms and counted the steps that the walker completed each time We denote a trial
as successful if the walker manages to make five to seven steps before it exits the ramp
While five to seven steps may seem short, we postulate that after five steps, the walker has
achieved a steady gait, and would ideally continue assuming a longer ramp existed
However, the impracticality of a longer ramp led us to set this number of steps as the
criteria for deciding walk success Fig 9 shows a comparison between the two knee
mechanism designs in terms of average number of steps made in each of the hundred trials
As the results show, using the knee mechanism with active release, we can achieve a
reasonable amount of successful trials Out of a hundred trials, the walker achieved an
average of forty-four successful walks with the active release system, while the magnetic
approach resulted in only seven In addition, using the active mechanism produces fewer
failures than the magnetic one
Fig 8 Walker on the ramp, outfitted with knees with active release system
Fig 9 Comparison between the experimental results achieved with the two mechanisms
Trang 12There are several types of reasons for a failed trial in general One is an incorrect start of the
walker by the person performing the experiments As this is done manually, it is subjective
and depends on the experience of the starter In case of an incorrect start the walker fails on
the first or the second step of the walk If the walker is started correctly and goes beyond the
first couple of steps it enters a stable gait and from this moment onwards there are two other
possible reasons for failure, which may occur at any time One is slippage of the foot against
the slope, which may be attributed to dirt or other obstacles present on it Another is failure
to lock or unlock the knee Failure to lock the knee is usually caused by the so-called knee
bouncing That is, when the knee extends too fast, the knee plate bounces off the knee, and
the locking hook has no time to lock it in place We have tried to reduce this to a minimum
by adding a small 1mm rubber mat to the knee face to cushion the hit Failure to unlock the
knee is mainly due to a late attempt to do it If the foot switch activates the DC motor after
the time when the knee starts to bend, the locking axle is already applying pressure to the
locking hook and it is unable to lift and release the knee By adjusting the foot switch to
activate earlier in the walking cycle we have significantly reduced the occurrence of this
problem
5 Discussion
In this chapter we presented two knee mechanism designs One features a permanent
magnet locking system and the other an active release system We performed a series of
experiments with both mechanisms mounted on the same passive-dynamic walking
machine and compared the results we achieved
The first knee mechanism was based on permanent magnets We speculated that changing
the distance between a permanent magnet and a steel plate, and hence changing the
magnetic force, would be sufficient to control the release moment of the knee with this
passive magnetic mechanism The experiments showed that the walker using this
mechanism was never able to make more than five steps and was only able to make a
successful trial, as defined earlier in the paper, in seven out of a hundred attempts As a
result of what we observed in several sets of experiments we have reached the conclusion
that it was very difficult to precisely setup and reliably uses the machine in the
configuration with the magnetic knee mechanism Ultimately, we decided to design and
build a completely different mechanism, with actively powered knee release action, which is
much simpler and more robust
Our design of the knee mechanism with active release showed promising results in the
experiments Even though we observed some variation of the number of successful trials, it
is obvious, that although not entirely passive, the new mechanism is more efficient in terms
of the walker managing to walk the entire length of the ramp when compared with the
previous design based on the entirely passive, magnetic lock The active release approach
allows the walker to achieve longer, more stable walks and is more robust and reliable We
performed several sets of a hundred trials and managed to achieve an average of forty-four
successes Using the proposed design we were also able to obtain a more even distribution
between trials of five, six, and seven step walks achieved by the walker The experimental
results show that the walker, equipped with the new knee-locking mechanism makes five or
more steps in a higher percentage of the trials Also the unsuccessful trials were greatly
reduced
Our goal from the start of this research was to prove that it is possible to design a simple and usable passive-dynamic walker without any complex modeling and simulations We wanted to see if the trial and error method would work for passive-dynamic walking where the stability range of the actual machines is very narrow The results show clearly that there
is an obvious improvement going from the first design to the second one This means that if the work continues in the same way additional improvement is possible
Our plans for the future include adding active control of the knee release system and building a starting mechanism for the walker in order to be able to control the release moment precisely and to reduce the failure rate even further We are already working on adding a controller and hip motor to the walker Our goal is set on achieving a highly successful walk on the experimental ramp and eventually on a flat surface
6 Acknowledgement
This research was also supported by Waseda University Grant for Special Research Projects, No.2008B-094, the Grant-in-Aid for the WABOT-HOUSE Project by Gifu Prefecture, the JSPS 21st Century Center of Excellence Program, ”The innovative research on symbiosis technologies for human and robots in the elderly dominated society” and the JSPS Global Center of Excellence Program, “Global Robot Academia”
7 References
A Baines, Knee Design for a Bipedal Walking Robot Based on a Passive-Dynamic Walker
B.S Thesis, Department of Mechanical Engineering, MIT, (2005)
S H Collins, A L Ruina, R Tedrake, M Wisse Efficient bipedal robots based on
passive-dynamic Walkers Science magazine, vol 307 pp 1082-1085, (2005)
S H Collins, A Ruina A bipedal walking robot with efficient and human-like gait In Proc
IEEE ICRA 2005, pp 1983 – 1988, Barcelona, Spain, (2005)
Y Ikemata, A Sano, Hideo Fujimoto, Generation and Local Stabilization of Fixed Point
Based on a Stability Mechanism of Passive Walking, Proc of ICRA 2007, pp
3218-3223, Rome, Italy (2007)
Y Ikemata, K Yasuhara, A Sano, Hideo Fujimoto, A study of the leg-swing motion of
passive walking, Proc of ICRA 2008, pp 1588-1593, Pasadena, USA, (2008)
T McGeer Passive dynamic walking International Journal of Robotics Research, 9(2)
pp.62-82, (1990)
K Trifonov, S Hashimoto, Design Improvements in Passive-Dynamic Walkers, In Proc
International Conference "Automatics and Informatics '06", Sofia, Bulgaria, pp
35-38, (2006)
K Trifonov, S Hashimoto, Active knee-lock release for passive-dynamic walking machines,
In Proc IEEE Robio 2007, pp 958-963, Sanya, China, (2007)
M Wisse, J V Frankenhuyzen Design and construction of Mike: a 2D autonomous biped
based on passive dynamic walking In Proc 2nd Int Symp on AMAM, Kyoto, Japan, (2003)
M Wisse, Essentials of dynamic walking Analysis and design of two-legged robots Ph.D
Thesis, Technische Universiteit Delft, (2004)
Trang 13There are several types of reasons for a failed trial in general One is an incorrect start of the
walker by the person performing the experiments As this is done manually, it is subjective
and depends on the experience of the starter In case of an incorrect start the walker fails on
the first or the second step of the walk If the walker is started correctly and goes beyond the
first couple of steps it enters a stable gait and from this moment onwards there are two other
possible reasons for failure, which may occur at any time One is slippage of the foot against
the slope, which may be attributed to dirt or other obstacles present on it Another is failure
to lock or unlock the knee Failure to lock the knee is usually caused by the so-called knee
bouncing That is, when the knee extends too fast, the knee plate bounces off the knee, and
the locking hook has no time to lock it in place We have tried to reduce this to a minimum
by adding a small 1mm rubber mat to the knee face to cushion the hit Failure to unlock the
knee is mainly due to a late attempt to do it If the foot switch activates the DC motor after
the time when the knee starts to bend, the locking axle is already applying pressure to the
locking hook and it is unable to lift and release the knee By adjusting the foot switch to
activate earlier in the walking cycle we have significantly reduced the occurrence of this
problem
5 Discussion
In this chapter we presented two knee mechanism designs One features a permanent
magnet locking system and the other an active release system We performed a series of
experiments with both mechanisms mounted on the same passive-dynamic walking
machine and compared the results we achieved
The first knee mechanism was based on permanent magnets We speculated that changing
the distance between a permanent magnet and a steel plate, and hence changing the
magnetic force, would be sufficient to control the release moment of the knee with this
passive magnetic mechanism The experiments showed that the walker using this
mechanism was never able to make more than five steps and was only able to make a
successful trial, as defined earlier in the paper, in seven out of a hundred attempts As a
result of what we observed in several sets of experiments we have reached the conclusion
that it was very difficult to precisely setup and reliably uses the machine in the
configuration with the magnetic knee mechanism Ultimately, we decided to design and
build a completely different mechanism, with actively powered knee release action, which is
much simpler and more robust
Our design of the knee mechanism with active release showed promising results in the
experiments Even though we observed some variation of the number of successful trials, it
is obvious, that although not entirely passive, the new mechanism is more efficient in terms
of the walker managing to walk the entire length of the ramp when compared with the
previous design based on the entirely passive, magnetic lock The active release approach
allows the walker to achieve longer, more stable walks and is more robust and reliable We
performed several sets of a hundred trials and managed to achieve an average of forty-four
successes Using the proposed design we were also able to obtain a more even distribution
between trials of five, six, and seven step walks achieved by the walker The experimental
results show that the walker, equipped with the new knee-locking mechanism makes five or
more steps in a higher percentage of the trials Also the unsuccessful trials were greatly
reduced
Our goal from the start of this research was to prove that it is possible to design a simple and usable passive-dynamic walker without any complex modeling and simulations We wanted to see if the trial and error method would work for passive-dynamic walking where the stability range of the actual machines is very narrow The results show clearly that there
is an obvious improvement going from the first design to the second one This means that if the work continues in the same way additional improvement is possible
Our plans for the future include adding active control of the knee release system and building a starting mechanism for the walker in order to be able to control the release moment precisely and to reduce the failure rate even further We are already working on adding a controller and hip motor to the walker Our goal is set on achieving a highly successful walk on the experimental ramp and eventually on a flat surface
6 Acknowledgement
This research was also supported by Waseda University Grant for Special Research Projects, No.2008B-094, the Grant-in-Aid for the WABOT-HOUSE Project by Gifu Prefecture, the JSPS 21st Century Center of Excellence Program, ”The innovative research on symbiosis technologies for human and robots in the elderly dominated society” and the JSPS Global Center of Excellence Program, “Global Robot Academia”
7 References
A Baines, Knee Design for a Bipedal Walking Robot Based on a Passive-Dynamic Walker
B.S Thesis, Department of Mechanical Engineering, MIT, (2005)
S H Collins, A L Ruina, R Tedrake, M Wisse Efficient bipedal robots based on
passive-dynamic Walkers Science magazine, vol 307 pp 1082-1085, (2005)
S H Collins, A Ruina A bipedal walking robot with efficient and human-like gait In Proc
IEEE ICRA 2005, pp 1983 – 1988, Barcelona, Spain, (2005)
Y Ikemata, A Sano, Hideo Fujimoto, Generation and Local Stabilization of Fixed Point
Based on a Stability Mechanism of Passive Walking, Proc of ICRA 2007, pp
3218-3223, Rome, Italy (2007)
Y Ikemata, K Yasuhara, A Sano, Hideo Fujimoto, A study of the leg-swing motion of
passive walking, Proc of ICRA 2008, pp 1588-1593, Pasadena, USA, (2008)
T McGeer Passive dynamic walking International Journal of Robotics Research, 9(2)
pp.62-82, (1990)
K Trifonov, S Hashimoto, Design Improvements in Passive-Dynamic Walkers, In Proc
International Conference "Automatics and Informatics '06", Sofia, Bulgaria, pp
35-38, (2006)
K Trifonov, S Hashimoto, Active knee-lock release for passive-dynamic walking machines,
In Proc IEEE Robio 2007, pp 958-963, Sanya, China, (2007)
M Wisse, J V Frankenhuyzen Design and construction of Mike: a 2D autonomous biped
based on passive dynamic walking In Proc 2nd Int Symp on AMAM, Kyoto, Japan, (2003)
M Wisse, Essentials of dynamic walking Analysis and design of two-legged robots Ph.D
Thesis, Technische Universiteit Delft, (2004)
Trang 15The human hand is the most dexterous and versatile biomechanical device that possesses
the human body, this device created by Nature during millions years of evolution
represents one of the more distinctive qualities among other animals Since the 70s and 80s,
important contributions have appeared in physiological studies of the human hand (I A
Kapandji, 1970), (I A Kapandji, 1981) Studies about robotic hands have made several
contributions e.g the Stanford/JPL hand (K S Salisbury & B Roth, 1983), the Utah hand (S
C Jacobsen et al., 1986), the Okada hand (T Okada, 1982), the Belgrade/USC hand (G
Bekey et al., 1990), the UB hands (C Melchiorri and G Vassura 1992), (C Melchiorri and G
Vassura 1993), the DLR hands (J Butterfass et al., 1999), (J Butterfass et al., 2001), the
University of Tokyo hand (Y K Lee & I Shimoyama, 1999), Barrett Hand (W T Townsend,
2000), the Robo-Naut hand by NASA (C S Lovchik et al., 2000), the Karlsruhe University
ultra-light hand (S Schulz et al., 2001), the GIFU hand (H Kawasaki et al., 2001), the
Shadow Dextrous Hand (Shadow Robot Company), (F Röthling et al., 2007), a prosthetic
hand (H Yokoi et al., 2004), the DLR-HIT-Hand (H Liu et al., 2008) and other These devices
have different kinematic configurations with respect to the number of Degrees of Freedom
(DoF) controlled, number of fingers, number of joints, type of actuation, etc This chapter
describes simplified human hand models that properly represent the kinematic behaviour of
the human hand in accordance with the precision and application required The first part
describes a human hand model with 24 DoF This model represents a balance between
complexity and realism Simplified human hand (SHH) models are analyzed using the
model with 24 DoF These SHH models (1 to 24 DoF) are evaluated in accordance with the
level of dexterous or power required A Cyberglove® (Immersion) is used for the
experiments carried out in this work Kinematic constrainswere checked with the
information provided by the glove Also, this glove was used for evaluating the error of the
SHH versus the full 24 DoF hand model Finally, the experiments carried out with SHH and
24 DoF hand model compare the efficiency in grasping for circular and prismatic grasps in
accordance with the application
10