Prototyping Pneumatic Group Actuators Composed of Multiple Single-motion Elastic Tubes

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1 Prototyping Pneumatic Group Actuators Composed of Multiple Single-motion Elastic Tubes Shinichi Hirai, Tomohiro Masui, and Sadao Kawamura Dept. of Robotics, Ritsumeikan Univ., Kusatsu, Shiga , Japan hirai/ Abstract In this article, we will develop pneumatic actuators composed of multiple elastic tubes. Elastic tubes with mechanical constraints have a capability of performing a single various motion while multiple motions cannot be performed. Actuators composed of single-motion tubes can realize multiple motions by controlling air pressure imposed on individual tubes. We will present the concept of group actuators and will develop their prototypes. 1 Introduction Actuators with high power/weight ratio have been required in many areas. For example, mechanical systems that support human motion in rehabilitation, welfare, and sports are under development. These mechanical systems are attached to a human body in order to provide a supporting motion to the body. Actuators used in these systems thus should have high power/weight ratio. Moreover, mechanical systems for entertainment requires various, smooth motions. Actuators applied to these systems also should have high power/weight ratio. In traditional design of mechanical systems, actuators generate a simple motion such as rotation or translation and the generated simple motion is converted into a specified motion through transmission mechanisms including gears, cams, and link mechanisms. Transmission mechanisms are usually of large weight that power/weight ratio of a total mechanical system including actuators and transmission mechanisms remains low. Consequently, actuators that can generate a specific motion directly without transmission mechanisms are required to increase the power/weight ratio of total mechanical systems. In the past decades, various pneumatic actuators such as braided actuators [1, 2], FMA [3], Flexator [4], HRA [5], and twisters [6] have been developed to generate a specific motion directly. These actuators consist of elastic shells with mechanical constraints, which convert air pressure into a specific motion. This suggests that elastic shells expanded by air pressure have a capability of generating various motion directly by imposing mechanical constraints on the shells. Unfortunately, elastic tubes with mechanical constraints can produce a single motion while multiple motions cannot be generated. In this article, we will develop pneumatic group actuators composed of multiple single-motion elastic tubes. Pneumatic group actuators have a capability of performing multiple motions by controlling air pressure imposed on individual tubes. First, we will systematically investigate the behavior of elastic tubes with mechanical constraints. Second, we will propose the concept of pneumatic group actuators. Two prototypes of pneumatic group actuators are then developed. Finally, the behavior of the two prototypes are investigated experimentally. 2 Single-motion Elastic Tubes Elastic tubes expanded by air pressure with mechanical constraints can generate various single motions directly. For example, an elastic tube with one axial fiber constraint, which is denoted as XF in Figure 1, perform bend motion by imposing air pressure inside the tube. These tubes are referred to as singlemotion tubes. Basic constraints on an elastic tube are enumerated in Figure 1. Individual basic constraints are denoted by constraint topology [7], as described in the figure. An arbitrary set of constraints are then described by a combination of basic constraints. Figure 2 shows some examples of combined constraints. Specifying an appropriate set of constraints on an elastic tube, various single motions including extension, shrinkage, bend, and twist can be generated directly. Figure 3 demonstrates the motion of an elastic tube with constraint topology XF-CF. The tube is made of silicon rubber. The inside diameter of the tube is equal to 10mm and the outside diameter is equal to 18mm. The tube is thus 4mm in thickness. As shown in Figure 3-(a), one axial fiber and multiple circular fibers are embedded in the tube. These fibers for constraint are embedded in the middle of the silicon rubber shell. Figure 3-(b) shows the deformed shape of the tube at air pressure of 0.05MPa and Figure 3-(c) describes the deformed shape at 0.12MPa. It turns out that an elastic tube with constraint XF-CF generates a bend motion. Figure 4 demonstrates the motion of an elastic

XF YF XmF YmF AF (a) natural state (b) 0.

1: Basic constraints on elastic tube XF-YF XF-XmF XF-CF RF-LF

(b) RF LF (c) r180xf (d) r180xf l180xf Figure 6: Results of FEM

12MPa Figure 3: Single motion tube XF-CF (a) constraints (b) 0.

10MPa Figure 4: Single motion tube RF tube with constraint topology

pressure of 0.05MPa and 0.10MPa, respectively.

motion around the central axis of the tube.

The inside diameter of the tube is equal to 10mm and the outside

The inside hole is eccentric to the outside surface.

2 XF YF XmF YmF AF (a) natural state (b) 0.10MPa CF RF LF r180xf l180xf Figure 5: Eccentric rubber tube Figure 1: Basic constraints on elastic tube XF-YF XF-XmF XF-CF RF-LF r180xf-l180xf Figure 2: Examples of combined constraints (a) XF CF (b) RF LF (c) r180xf (d) r180xf l180xf Figure 6: Results of FEM simulation (a) constraints (b) 0.05MPa (c) 0.12MPa Figure 3: Single motion tube XF-CF (a) constraints (b) 0.05MPa (c) 0.10MPa Figure 4: Single motion tube RF tube with constraint topology RF. As shown in Figure 4-(a), one spiral fiber is embedded in an elastic tube made of silicon rubber. Figure 4-(b) and (c) show the deformed shapes of the tube at air pressure of 0.05MPa and 0.10MPa, respectively. We find that an elastic tube with constraint RF generates a twist motion around the central axis of the tube. Figure 5 shows the motion of an eccentric silicon tube. The inside diameter of the tube is equal to 10mm and the outside diameter is equal to 18mm. The inside hole is eccentric to the outside surface. Consequently, the thickness of the tube is 6mm in the left side while it is 2mm in the right side. No fiber constrains are embedded in the tube. As shown in Figure 5, it has shown that a bend motion can be generated by an eccentric tube. Let us analyze the deformation of elastic tubes with mechanical constraints through FEM simulation. Two finite elements are used in the simulation; one for an elastic cylindrical surface and the other for fibers. Figure 6-(a) describes the motion of an elastic tube

moving F1 S2 S3 elastic tubes F2 F1 moving elastic tubes elastic tubes S1 F3 S2 F2 S3 F1 middle fixed F3 F2 S1 (a) tubes on fixed (b) tubes on middle Figure 8: Tube symbols (a) Single-stage fixed (b)

XF-CF. Recall that constraint XF generates bend motion with expansion of the tube. As shown in the figure, an elastic tube with constraint XF-CF yields bend motion with little expansion.

3 moving F1 S2 S3 elastic tubes F2 F1 moving elastic tubes elastic tubes S1 F3 S2 F2 S3 F1 middle fixed F3 F2 S1 (a) tubes on fixed (b) tubes on middle Figure 8: Tube symbols (a) Single-stage fixed (b) Double-stage Figure 7: Prototypes of pneumatic group actuator natural F1 F2 F3 F1 F2 F3 Figure 9: Topologically different pressure patterns of single-stage group actuator with a combined constraints XF-CF. Recall that constraint XF generates bend motion with expansion of the tube. As shown in the figure, an elastic tube with constraint XF-CF yields bend motion with little expansion. Namely, constraint CF suppresses the expansion. Figure 6-(b) describes the motion of an elastic tube with a combined constraints LF-RF. As shown in the figure, the tube generates shrinking motion of the tube. Figure 6-(c) provides the motion of an elastic tube with a basic constraint r180xf. Note that this tube yields translational motion. Figure 6- (d) shows the motion of an elastic tube with a combined constraints r180xf-l180xf. Namely, two spiral constraints are embedded in the tube. As shown in the figure, this tube generates translational motion. The above examples have demonstrated that various single motions can be generated by embedding constraints in an elastic tube or by designing the shape of an elastic tube. 3 Pneumatic Group Actuators As mentioned in the previous section, we can realize an elastic tube that generates a various single motion by designing constraints on the tube as well as the shape of the tube. However, each tube can yield a single motion and cannot generate multiple motions. One approach to the generation of multiple motions by one tube is the use of tunable constraints [8]. Bend rigidity or extensional rigidity of tunable constraints can be changed according to external signals. This implies that the rigidity of fiber constraints embedded in an elastic tube can be controlled and that the multiple motions are generated by changing the rigidity of individual constraints. Unfortunately, the rigidity of current tunable constraints is insufficient to elastic tubes expanded by air pressure. Another approach to the generation of multiple motions is to combine single-motion elastic tubes and to control air pressure applied to the tubes individually. Actuators composed of multiple single-motion tubes are referred to as pneumatic group actuators. Pneumatic group actuators consist of multiple s and single-motion elastic tubes connecting the s. Imposing air pressure on individual tubes causes different deformations of the tubes, which result in multiple motions of the end. Prototypes of pneumatic group actuators are shown in Figure 7. Prototype shown in Figure 7-(a) consists of two s, say, the fixed and the moving, and three silicon tubes. This prototype is referred to as a single-stage pneumatic group actuator. Plates are made of aluminum and their diameter is equal to 55mm. Elastic tubes can be mounted on a through couples. The couples are 10mm or 12mm in diameter. Arbitrary tubes including elastic tubes with fiber constraints as well as eccentric tubes are available once they can be inserted into the couples. Prototype shown in Figure 7-(b) consists of three s, say, the fixed, the middle, and the moving, natural S1 S23 S123 F1 F1 S1 F1 S2 F1 S23 F1 S12 F1 S123 F23 F23 S1 F23 S2 F23 S23 F23 S12 F23 S123 F123 F123 S1 F123 S23 F123 S123 Figure 10: Topologically different pressure patterns of double-stage group actuator

F1 0.09MPa 0.09MPa 0.09MPa 0.07MPa 0.05MPa F2 0.05MPa 0.07MPa 0.09MPa 0.09MPa 0.09MPa F3 0.05MPa 0.07MPa 0.09MPa 0.09MPa 0.09MPa (a) (b) (c) (d) (e) Figure 11: Behavior of single-stage pneumatic group actuator and six silicon tubes.

Single-motion tubes in the prototypes are referred to as shown in Figure 8.

A double-stage group actuator involves F1, F2, F3, S1, S2, and S3. Motion of the prototypes is specified by air pressure at these tubes.

Considering the symmetry of tube locations, we have four topologically different patterns as illustrated in the figure.

Patterns F1 and F2-F3 generate bend motion of the moving. Pattern F1-F2-F3 yields its extensional motion. Let us investigate the motion of a double-stage group actuator qualitatively.

4 F1 0.09MPa 0.09MPa 0.09MPa 0.07MPa 0.05MPa F2 0.05MPa 0.07MPa 0.09MPa 0.09MPa 0.09MPa F3 0.05MPa 0.07MPa 0.09MPa 0.09MPa 0.09MPa (a) (b) (c) (d) (e) Figure 11: Behavior of single-stage pneumatic group actuator and six silicon tubes. Three tubes connect the fixed and the middle while the others connect the middle and the moving. This prototype is referred to as a double-stage pneumatic group actuator. Single-motion tubes in the prototypes are referred to as shown in Figure 8. Tubes on the fixed are denoted as F1, F2, and F3 while tubes on the middle are denoted as S1, S2, and S3, as illustrated in the figure. A single-stage group actuator then involves F1, F2, and F3. A double-stage group actuator involves F1, F2, F3, S1, S2, and S3. Motion of the prototypes is specified by air pressure at these tubes. Let us investigate the motion of a single-stage group actuator qualitatively. Figure 9 describes patterns of air pressure applied to individual tubes. Considering the symmetry of tube locations, we have four topologically different patterns as illustrated in the figure. Air pressure is applied to black tubes in the figure while it is not applied to white tubes. Assume that the three tubes are plain ones, say, uniform elastic tubes with no constraints. Patterns F1 and F2-F3 generate bend motion of the moving. Pattern F1-F2-F3 yields its extensional motion. Let us investigate the motion of a double-stage group actuator qualitatively. Figure 10 describes patterns of air pressure imposed on individual tubes. Considering the symmetry of tube locations, we have twenty topologically different patterns as enumerated in the figure. For the sake of simplicity, pattern F2-F3 is abbreviated as F23, and so on. Assuming that the six tubes are plain ones, we find that patterns F1, F23, S1, and S23 generate bend motion of the moving. Patterns F1-S23 and F23-S1 generate larger bend motion since both the first stage and the second stage yield bend motion. Bend motion at the first stage cancels bend motion at the second stage in patterns F1-S1 and F23-S23. Consequently, patterns F1-S1 and F23-S23 generate translational motion of the moving. Direction of bend motion at the first stage is not parallel to that of bend motion at the second stage in patterns F1-S2, F1-S12, F23-S2, and F23-F12. Thus, patterns F1-S2, F1-S12, F23-S2, and F23-F12 produce twisted bend motion. Patterns F123, S123, and F123-S123 yield extensional motion. Bend motion is generated at the first stage and extensional motion is generated at the second stage in patterns F1-S123 and F23-S123. Extensional motion is generated at the first stage and bend motion is generated at the second stage in patterns F123-S1 and F123-S23. Thus, patterns F1-S123, F23-S123, F123-S1, and F123-S23 produce extensional bend motion of the moving. As a result, we find that a double-stage group actuator with plain elastic tubes has a capability of performing bend, extension, and translation of the moving while it cannot generate shrinkage and twist around the central axis. 4 Experiments In this section, we will experimentally evaluate the behavior of the proposed prototypes of pneumatic group actuators. Let us first investigate the behavior of a single-stage pneumatic group actuator. Tubes installed between the fixed and the moving are plain ones with 14mm in outside diameter, 10mm in inside diameter, and 60mm in length. The singlestage prototype then weighs 195g. Let us apply air pressure to individual tubes F1, F2, and F3, as given in Figure 11. Behavior of a single-stage group actuator corresponding to given air pressure is described in the figure as well. It turns out that the center of the moving moves along a circle. The inclination angle of the moving takes its maximum value 20 at Figure 11-(a). Let us next investigate the behavior of a doublestage pneumatic group actuator. This double-stage prototype weighs 290g totally. Let us apply air pressure 0.08MPa to some tubes of the six and 0.00MPa to the other tubes. Figure 12-(a) shows the natural state of the double-stage group actuator. Air pressure 0.08MPa is imposed on tube F2 alone in Figure 12-(b). Note that the moving remains parallel

Figure 12: (a) natural state (c) S2 (b) F2 (d) F2 S2 Behavior of double-stage pneumatic group actuator to the middle since no air pressure is applied to tubes S1, S2, and S3. Air pressure 0.

08MPa is applied to two tubes F2 and S2 in Figure 12-(d). Note that this pressure pattern coincides to F1-S1 in Figure 10. Recall that pattern F1-S1 produces translation of the moving.

Air pressure is applied to three tubes F1, F2, and S3. Figure 13-(a) describes the natural state of the actuator. Air pressure from 0.00MPa to 0.12MPa is applied to the three tubes.

Figure 14 demonstrates the translational motion of a doublestage group actuator. Air pressure is applied to four tubes F1, F2, S1, and S2. Figure 14-(a) describes the natural state of the actuator.

5 Figure 12: (a) natural state (c) S2 (b) F2 (d) F2 S2 Behavior of double-stage pneumatic group actuator to the middle since no air pressure is applied to tubes S1, S2, and S3. Air pressure 0.08MPa is applied to tube S2 alone in Figure 12-(c). Note that the middle remains at its natural location since no air pressure is applied to tubes F1, F2, and F3. Air pressure 0.08MPa is applied to two tubes F2 and S2 in Figure 12-(d). Note that this pressure pattern coincides to F1-S1 in Figure 10. Recall that pattern F1-S1 produces translation of the moving. Here we have experimentally proved that the double-stage group actuator can generate translational motion. Figure 13 demonstrates the bend motion of a double-stage group actuator. Air pressure is applied to three tubes F1, F2, and S3. Figure 13-(a) describes the natural state of the actuator. Air pressure from 0.00MPa to 0.12MPa is applied to the three tubes. Figure 13-(b) through Figure 13-(h) show the deformed shapes. The inclination angle of the moving is almost 80 in Figure 13-(h). Figure 14 demonstrates the translational motion of a doublestage group actuator. Air pressure is applied to four tubes F1, F2, S1, and S2. Figure 14-(a) describes the natural state of the actuator. Air pressure from 0.00MPa to 0.12MPa is applied to the four tubes. Figure 14-(b) through Figure 14-(h) show the deformed shapes. The moving place translates 20 % with respect to the total height of the actuator. From the above experiments, we have found that a double-stage pneumatic group actuator composed of plain elastic tubes has a capability of generating bend motion and translational motion. 5 Concluding Remarks We have proposed pneumatic group actuators and have developed their prototypes. First, we have investigated the behavior of single-motion elastic tubes through experiments and FEM simulation. Then, we have prototyped pneumatic group actuators. The behavior of single-stage actuators and double-stage actuators is analyzed topologically and is investigated experimentally. We have concluded that a double-stage pneumatic group actuator has a capability of generating bend motion and translational motion. Static and dynamic properties of the prototyped pneumatic group actuators will be investigated to control the motion of the actuators. Moreover, we will develop group actuators composed of tubes with fiber constraints and eccentric tubes to investigate their behavior. Acknowledgement This research was supported in part by JSPS- RFTF from the Japan Society for the Promotion of Science. References [1] Chou, C. P. and Hannaford, B., Static and Dynamic Characteristics of McKibben Pneumatic Artificial Muscles, Proc. IEEE Int. Conf. on Robotics and Automation, Vol.1, pp , San Diego, May, 1994 [2] Tsagarakis, N. and Caldwell, D. G., Improved Modelling and Assessment of Pneumatic Muscle Actuators, Proc. IEEE Int. Conf. on Robotics and Automation, pp , San Francisco, April, 2000 [3] Suzumori, K., Iikura, S., and Tanaka, H., Development of Flexible Microactuator and Its applications to Robotic Mechanisms, Proc. IEEE Int. Conf. on Robotics and Automation, Vol.2, pp , Sacramento, April, 1991 [4] Ouerfelli, M., Kumar, V., and Harwin, W., An Inexpensive Pneumatic Manipulator for Rehabilitation Robotics, Proc. IEEE Int. Conf. on Robotics and Automation, Vol.1, pp , Atlanta, May, 1993 [5] Shimizu, T., Hayakawa, Y,, and Kawamura, S., Development of a Hexahedron Rubber Actuator, Proc. IEEE Int. Conf. on Robotics and Automation, pp , Nagoya, May, 1995 [6] Paynter, H. M., Low-Cost Pneumatic Arthrobots Powered by Tug-and-Twist Polymer Actuators, Proc. Japan-U.S.A. Symp. on Flexible Automation, Vol.1, pp , Otsu, July, 1996 [7] Hirai, S., Tanigawa, H., Cusin, P., Masui, T., Konishi, S., and Kawamura, S., Qualitative Synthesis of Deformable Cylindrical Actuators through Constraint Topology, Proc. IEEE/RSJ Int. Conf. on Intelligent Robots and Systems, Vol.1, pp , Takamatsu, October, 2000 [8] Tabata, T., Konishi, S., Cusin, P., Ito, Y., Kawai, F., Hirai, S., and Kawamura, S., Microfabricated Tunable Bending Stiffness Device, Proc. IEEE 13th Annual Int. Conf. on Micro ElectroMechinical Systems, pp.23 27, Miyazaki, January, 2000

6 (a) 0.00MPa (b) 0.05MPa (c) 0.07MPa (d) 0.08MPa (e) 0.09MPa (f) 0.10MPa (g) 0.11MPa (h) 0.12MPa Figure 13: Bend motion of double-stage pneumatic group actuator (a) 0.00MPa (b) 0.05MPa (c) 0.07MPa (d) 0.08MPa (e) 0.09MPa (f) 0.10MPa (g) 0.11MPa (h) 0.12MPa Figure 14: Translational motion of double-stage pneumatic group actuator

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