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A New Self-Loading Locomotion Mechanism for Wall Climbing Robots Employing Biomimetic Adhesives
Journal of Bionic Engineering 10 (2013) 12–18
A New Self-Loading Locomotion Mechanism for Wall Climbing Robots Employing Biomimetic Adhesives Amirpasha Peyvandi1, Parviz Soroushian1, Jue Lu2 1. Department of Civil and Environmental Engineering, Michigan State University, 3546 Engineering Building, E. Lansing, MI 48824-1226, USA 2. Senior Scientist, Technova Corporation, 1926 Turner Street, Lansing, MI 48906, USA
Abstract A versatile locomotion mechanism is introduced and experimentally verified. This mechanism comprises four rectangular wheels (legs) with rotational phase difference which enables the application of pressure to each contacting surface for securing it to the surface using bio-inspired or pressure-sensitive adhesives. In this mechanism, the adhesives are applied to two rigid plates attached to each wheel via hinges incorporating torsional springs. The springs force the plates back to their original position after the contact with the surface is lost in the course of locomotion. The wheels are made of low-modulus elastomers, and the pressure applied during contact is controlled by the elastic modulus, geometry and phase difference of wheels. This reliable adhesion system does not rely upon gravity for adhering to surfaces, and provides the locomotion mechanism with the ability to climb walls and transition from horizontal to vertical surfaces. Keywords: biomimetics, adhesives, locomotion, climbing robots, gecko Copyright © 2013, Jilin University. Published by Elsevier Limited and Science Press. All rights reserved. doi: 10.1016/S1672-6529(13)60194-8
1 Introduction There is a great interest in developing versatile locomotion capabilities for (unmmaned) micro air vehicles (when landed) and also for micro robots and unmanned ground vehicles[1–4]. These vehicles can replace human in high-risk or remote work environments like high-rise buildings[5,6], and nuclear power plants[3,7] or in special tasks such as inspection, surveillance and reconnaissance[8]. Over the years, a great number of locomotion mechanisms have been proposed for traversing rugged horizontal or vertical surfaces[3]. A key consideration in designing such systems is the ability to climb vertical surfaces. Three major adhesion concepts have been considered for making use of these locomotion mechanisms: vacuum suction[9–13], magnetic attraction[14–17], and grasping/gripping with claws[18–20]. There are some advantages and drawbacks associated with each of these mechanisms. Vacuum suction is used widely because of its simple structure and control [11,23] ; this mechanism, however, requires a smooth surCorresponding author: Amirpasha Peyvandi E-mail: [email protected]
face to ensure sealing, and its untethered climbing duration is limited by power efficiency. Magnetic adhesion can be very strong, but it is limited to ferromagnetic surfaces. Micro claws are also limited to very rough surfaces such as brick and stone, but they can not function on smooth surfaces such as glass or painted wall. Recently, some progress has been made in locomotion against various types of surfaces with different roughness conditions by using an emerging generation of dry bio-inspired adhesive materials[28] comprising fibrillar arrays, which are similar to those used by geckos, spiders, flies and other insects[22–24]. Bio-inspired adhesive micro/nano-scale fibrillar structures provide high adhesion capacity against a great variety of surfaces at high reliability levels. Selfcleaning is an appealing feature of the fibrillar (inspired by the gecko-foot) adhesion mechanism[25–27]. Various locomotion mechanisms could benefit from the introduction of bio-inspired adhesives for energy-efficient and versatile locomotion against different surfaces[22,23,29–32]. The pressure applied during contact is an important
Peyvandi et al.: A New Self-Loading Locomotion Mechanism for Wall Climbing Robots Employing Biomimetic Adhesives
factor governing the adhesion capacity developed by bio-inspired adhesives (or traditional pressure-sensitive adhesives) against the surface. In this study, a locomotion mechanism (Fig. 1) was developed for streamlined application of the pressure required to bring the adhesive into intimate contact with surfaces of different inclinations and roughness conditions. This mechanism enables effective use of bio-inspired adhesives (as well as traditional pressure-sensitive adhesives) which offer desired qualities such as energy-efficient separation from the surface via peeling[33], ability to adhere to different surfaces, thermal stability[34], and self-cleaning attributes[26,27].
Fig. 1 The locomotion system with bio-inspired adhesives climbing a wall.
2 Mechanism of pressure application upon contact The contacting surfaces of plates connected to wheels are coated with peelable bio-inspired adhesives. These adhesives require application of a minimum pressure upon contact in order to effectively adhere to the surfaces of different types and roughness conditions. The approach adopted here uses the adhesion capacity of two (first group) of the wheels that have already adhered to the surface in order to apply pressure to the other two (second group of) wheels as they establish contact with the surface during locomotion. The first group of wheels would then peel off the surface, and the adhesion capacity of the second group would be used to apply pressure to them as they establish new contacts with the surface. This sequence of events would be repeated in the course of locomotion. The pressure applied to each group of wheels upon contact is equilibrated by the ten-
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sion generated in the other group of wheels, and it does not depend upon surface inclination and gravity. This enables the system to traverse the surfaces of different inclinations (e.g., climb walls). A wheel with two rigid plates (coated with bio-inspired fibrillar adhesive) is shown in Fig. 2. This wheel is made of an elastomer, and the geometry and elastic modulus of the wheel are selected for application of the required contact pressure during locomotion. The wheels in each of the two groups noted above are perpendicular to the wheels in other groups (i.e., the two groups of wheels have 90 degrees rotational phase difference). The difference between the length and width of rectangular wheels is thus the cause of pressure application on a group of wheels establishing contact with the surface during locomotion. In each elastomeric wheel (component 3 in Fig. 2), the contacting surface is that of a rigid plate (component 2 in Fig. 2) that is attached to the wheel via a hinge incorporating a rotational spring (component 5 in Fig. 2). The contacting surface of the plate is coated with a peelable bio-inspired (fibrillar) adhesive (component 1 in Fig. 2). As each plate established contact with the surface, the rotational spring allows it maintain contact with the surface as the wheel undergoes 90 degrees rotation. Afterwards, the plate peel off the surface during another 90 degrees of rotation, and the rotational spring returns it to its original position after it is peeled off the surface. Component 4 in Fig. 2 is a shaft that connects an axle to the wheel. 1
2
2(a+b)
4
2
1 t 3
5
3 2a 2
1
1
2 (a)
(b)
Fig. 2 Wheel (leg) components. (a) Front view; (b) side view.
3 Wheel (leg) design Each wheel in the locomotion mechanism contacts the surface (via plates coated with bio-inspired adhesive) with either its short face (with length 2a) or its long face (with length 2b) facing the surface (Fig. 3). Stiffness of the wheel (under loads normal to the surface applied via axle at mid-height) is a factor in determining the pressure applied upon contact for adherence to the surface.
Journal of Bionic Engineering (2013) Vol.10 No.1
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When the short side (width) of a wheel contacts the surface, this stiffness, K1 can be written as
Eat K1 = , b
(1)
where E is the elastic modulus of the wheel material, a and b are half the width and length of wheel, respectively, and t is the thickness of wheel. When the long side (length) of a wheel contacts the surface, the stiffness, K2 can be written as
Ebt K2 = , a
F1 = K1δ1 , F2 = K 2δ 2 , F3 = K 3δ 3 , F4 = K 4δ 4 ,
(4)
where δ1, δ2, δ3 and δ4 are the deformations of wheels 1, 2, 3 and 4, respectively, normal to the contact surface over the distance from axle to contact surface. With wheels of similar geometric and material characteristics, and neglecting the gravity effects, the configuration of Fig. 4 produces forces with equal absolute values (|F1|=|F2|=|F3|=|F4|). F2
F3
(2) F1 F4
Fig. 4 Schematic view of forces applied to the four wheels in a particular step during locomotion. Fig. 3 Schematic view of wheel with its dimensions.
Fig. 4 shows the orientations of the wheels in locomotion system. Fig. 4 also shows the forces applied to the wheels in a particular step during locomotion; neglecting the gravity forces would produce similar forces in horizontal, vertical or other configurations of the locomotion system. The applied forces are tensile in the case of wheels with their longer side (length) normal to the surface and they are compressive in the case of wheels with their shorter side (width) normal to the surface. These forces are applied via axles. The wheels receiving compressive forces are those just contacting the surface, and the compressive force generates the pressure required for adhering to the surface via adhesives (bio-inspired or pressure sensitive adhesives). The wheels receiving tensile forces are those that have already adhered to the surface, and their adhesion capacity is used to balance the compressive force applied on newly contacting wheels. The tensile and compressive forces shown in Fig. 4 should balance each other F1 + F3 = F2 + F4 .
(3)
The force developed in each wheel is equal to the product of the wheel stiffness and the wheel deformation in the direction of applied force
Since wheels 1 and 3, and also wheels 2 and 4 act similarly, this discussion focuses on wheels 1 and 2. For these two wheels, ⎛ Eat ⎞ ⎛ Ebt ⎞ K1δ1 = K 2δ 2 ⇒ ⎜ ⎟ δ1 = ⎜ ⎟δ2 . ⎝ b ⎠ ⎝ a ⎠
(5)
Hence,
δ1 b 2 = . δ 2 a2
(6)
Wheels 1 and 2, which are perpendicular to each other, undergo deflections δ1 and δ2 in order to overcome the difference between the distances of their axel from contact surface, that is ∆ = b−a. Hence,
δ1 + δ 2 = Δ ,
(7)
where δ1 and δ2 are expressed as absolute values. The above expressions enable derivation of one dimension of the rectangular wheel (e.g., half the width, b) in terms of its other dimension (e.g., half the length, a) and elastic modulus (E) in order to apply a targeted compressive force (F2) required for adhering to the bio-inspired adhesive to the contact surface, as described below. Eqs. (6) and (7) indicate (using the notation β = b2/a2)
Peyvandi et al.: A New Self-Loading Locomotion Mechanism for Wall Climbing Robots Employing Biomimetic Adhesives
δ1 =
β (b − a) , (1 + β )
(8)
δ2 =
(b − a ) . (1 + β )
(9)
The above equations can be used to derive (b) in terms of (a) and elastic modulus. This design requires the definition of gravity forces, which have been neglected so far. A viable design, however, would require consideration of gravity forces because the effects of gravity forces depend upon surface inclination, mass of the system, and the distance from the center of gravity of the mass to surface. At a critical point during locomotion, two of the wheels are adhered to the surface. These two wheels should be able to resist the tensile and shear forces applied under the combined effects of gravity and the balancing action of wheels described above. This requirement combined with the shear and tensile adhesion capacities of the bio-inspired adhesives would govern the determination of the total contact area of each wheel. This contact area is actually that of a plate connected to the wheel, which is coated with bio-inspired adhesive. Fig. 2 presents the plate geometry; its length is equal to 2(a+b) and its width is equal to the wheel thickness.
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180-degree rotation of the wheel uses the adhesion capacity of two in-phase wheels to apply pressure on the other two wheels (see Fig. 4). The forces in Fig. 4 are developed due to the phase difference between rotational angles of rectangular wheels connected to a rigid body via axles. The rotational phase difference generates height difference from the axle of each wheel to the contact surface. A more detailed illustration of the operation of one wheel in the locomotion mechanism of Fig. 1 is presented in Fig. 5. The wheel undergoes the four sequential steps shown in Fig. 5 as it undergoes 360 degrees rotation. The rotation of the hinged rigid plate (2a) is enabled by a torsional spring introduced at the hinge location (component 6a in Fig. 5). During the rotation of the wheel, the hinge incorporating the torsional spring is key to maintaining the adhered status of the plate (component 2a in Fig. 5) after the application of pre-load pressure as the wheel undergoes 90 degrees rotation before it peels off the surface as the next hinged plate (component 2b in Fig. 5) establishes contact and receives the pre-load pressure.
4 Kinematics of locomotion Referring to the Fig. 1, each wheel comprises a flexible (elastomeric) rectangular body (component 3 in Fig. 2), with different parts attached to it. These parts include two side plates (component 2 in Fig. 2), which are covered with adhesives (preferably bio-inspired fibrillar adhesives, or pressure-sensitive adhesives) (component 1 in Fig. 2). Two diagonally oriented wheels (see Fig. 1), which rotate around its axis (component 4 in Fig. 2), are in phase (i.e., have the same orientation), and the other two are 90 degrees out of phase with respect to them. The side plates at their attachment locations incorporate torsional springs (component 5 in Fig. 2) which restore their original inclinations after the plate peels off the surface in the course of wheel rotation. Each wheel has two rigid plates, each of which stays in contact with the surface over a rotation angle of 180 degrees. The use of solid plates improves the uniformity of pressure applied to the contact area. Upon separation, the torsional spring (component 5 in Fig. 2) restores the original inclination of the rigid plate. Each
Fig. 5 The sequential steps involved in the rotation of a wheel.
In step 1 (in Fig. 5), plate (2a) has established contact, and received the pre-load pressure required for adhering to the surface. In step 2, the plate has adhered to the surface, and its adhesion capacity is used to apply pre-load pressure to other wheels which are out of phase with respect to it. Plate (2a) remains in contact with the
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Journal of Bionic Engineering (2013) Vol.10 No.1
surface throughout steps 1 and 2. During transformation from step 2 to step 3, plate (2a) separates (peels off) from the surface, and the hinge (6a) incorporating torsional spring returns to the rest position of the torsional spring and brings plate (2a) into its rest position. In step 3, plate (2b) assumes the position of plate (2a) in step 1. In transition from step 3 to step 4, plate (2b) and hinge (6b) play the roles of plate (2a) and hinge (6a) in transition from step 1 to step 2. After step 4, the wheel configuration returns to step 1 because of incorporating torsional spring 6b which wants to return back to its rest position, and the four steps shown in Fig. 5 will be repeated.
The wheels were designed based on the theoretical work presented earlier and were fabricated by casting in molds (Fig. 7a). The side plates at their attachment locations (pins shown in Fig. 7a) incorporate torsional springs (Fig. 7b) which restore the original inclinations of plates after the contact with the surface is lost in the course of wheel rotation (locomotion). Fig. 8 shows two side views of the rectangular wheel with side plates. The side plates and the inclusions in polyurethane wheel were made of aluminum.
5 Experimental validation of the locomotion mechanism Self-loading locomotion mechanism employing bio-inspired adhesives was developed and evaluated. The vehicle embodying the self-loading locomotion mechanismis is 4.5 cm wide and 12.0 cm long[25]. This system has two axles accommodating a total of four wheel-legs. Both axles are driven by a single motor. A rack and pinion steering mechanism pivots the front wheel-legs. The rack and pinion system comprises a pair of gears which convert rotational motion into linear motion. The “pinion” engages teeth on a linear “gear” bar known as the “rack”; rotational motion applied to the pinion causes the rack to move, thereby this action could transfer to the front wheel. The electronics drive system and batteries are contained within the system, and its total weight (including wheels weight) is 130 grams. Fig. 6 shows the details of a rectangular wheel and its side plates. ST-3040 Polyurethane (BJB Enterprise, Inc.) was used for production of the rectangular wheels. This polyurethane has a tensile strength of 5.27 MPa, an elastic modulus of 0.69 MPa, and a hardness of 42 A.
Fig. 6 Geometry detailing of the new rectangular wheel.
Fig. 7 Wheel production and components. (a) Molds used for casting the elastomeric body of wheels; (b) torsional springs used at the pin location of side plates on elastomeric wheels.
Fig. 8 Side views of wheels comprising an elastomeric rectangular body and aluminum components. (a) Back view; (b) front view.
The locomotion mechanism incorporating four rectangular wheels is shown in Fig. 1 on a vertical glass surfaces. The side plates of wheels were covered with bio-inspired adhesives. These adhesives were fibrillar array, comprising fibrils 20 μm in length and 20 μm in diameter (Fig. 9). Tension and shear adhesion capacities of 1 cm × 1 cm specimens of fibrillar arrays which used in locomotion mechanism were measured against glass slides. The experimental was performed on three different samples. These substrates were sonicated in distilled water for 15 minutes, and then blown dried with N2 gas. A preload pressure of 5 kPa (5 N on 1 cm × 1 cm contacted area) was applied to establish adhesion prior to the performance of tension and shear adhesion tests. Based on the adhesion capacity provided by fibrillar array and locomotion system weight, the required bio-inspired adhesive (fibrillar array) was calculated and put on the bottom of each wheels. Developing fibrillar array could provide 25 kPa and 15 kPa shear and tensile adhesion capacity, respectively, against glass (Fig. 10).
Peyvandi et al.: A New Self-Loading Locomotion Mechanism for Wall Climbing Robots Employing Biomimetic Adhesives
Bio-inspired adhesive arrays with 1 cm × 5 cm planar dimensions were placed on the bottom of each plate. The system was evaluated by determining its ability to climb a vertical glass surface (Fig. 1). The locomotion system ascended the vertical surface about 90 cm at a speed of 4 cm·s−1 without falling.
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can provide unmanned (air or ground) vehicles with versatile mobility in difficult terrain and against inclined or vertical surfaces.
Acknowledgments The authors acknowledge the support of the U.S. Air Force (Contract FA8651-07-C-0092) for the project.
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6 Conclusion A new locomotion mechanism is presented, with wheels employing bio-inspired adhesives for operation against surfaces of different inclination and roughness conditions. This mechanism enables movement on vertical surfaces. The new locomotion mechanism provides the inherent ability to apply pressure on adhesives as they establish contact with the surface, without relying on gravity, in order to effectively adhere to various surfaces of different inclinations. Some of the wheels in this locomotion-mechanism have rotational phase difference with respect to the other wheels. At each moment, the in-phase wheels have established adhesion with the surface, and are used to apply pressure to the other wheels as they contact the surface. In order to validate this self-loading locomotion mechanism, prototype system was designed and fabricated using bio-inspired adhesives and was tested on vertical glass surfaces. The system ascended the vertical surface at a speed of 4 cm·s−1 without falling. This locomotion mechanism
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A New Self-Loading Locomotion Mechanism for Wall Climbing Robots Employing Biomimetic Adhesives Amirpasha Peyvandi1, Parviz Soroushian1, Jue Lu2 1. Department of Civil and Environmental Engineering, Michigan State University, 3546 Engineering Building, E. Lansing, MI 48824-1226, USA 2. Senior Scientist, Technova Corporation, 1926 Turner Street, Lansing, MI 48906, USA
Abstract A versatile locomotion mechanism is introduced and experimentally verified. This mechanism comprises four rectangular wheels (legs) with rotational phase difference which enables the application of pressure to each contacting surface for securing it to the surface using bio-inspired or pressure-sensitive adhesives. In this mechanism, the adhesives are applied to two rigid plates attached to each wheel via hinges incorporating torsional springs. The springs force the plates back to their original position after the contact with the surface is lost in the course of locomotion. The wheels are made of low-modulus elastomers, and the pressure applied during contact is controlled by the elastic modulus, geometry and phase difference of wheels. This reliable adhesion system does not rely upon gravity for adhering to surfaces, and provides the locomotion mechanism with the ability to climb walls and transition from horizontal to vertical surfaces. Keywords: biomimetics, adhesives, locomotion, climbing robots, gecko Copyright © 2013, Jilin University. Published by Elsevier Limited and Science Press. All rights reserved. doi: 10.1016/S1672-6529(13)60194-8
1 Introduction There is a great interest in developing versatile locomotion capabilities for (unmmaned) micro air vehicles (when landed) and also for micro robots and unmanned ground vehicles[1–4]. These vehicles can replace human in high-risk or remote work environments like high-rise buildings[5,6], and nuclear power plants[3,7] or in special tasks such as inspection, surveillance and reconnaissance[8]. Over the years, a great number of locomotion mechanisms have been proposed for traversing rugged horizontal or vertical surfaces[3]. A key consideration in designing such systems is the ability to climb vertical surfaces. Three major adhesion concepts have been considered for making use of these locomotion mechanisms: vacuum suction[9–13], magnetic attraction[14–17], and grasping/gripping with claws[18–20]. There are some advantages and drawbacks associated with each of these mechanisms. Vacuum suction is used widely because of its simple structure and control [11,23] ; this mechanism, however, requires a smooth surCorresponding author: Amirpasha Peyvandi E-mail: [email protected]
face to ensure sealing, and its untethered climbing duration is limited by power efficiency. Magnetic adhesion can be very strong, but it is limited to ferromagnetic surfaces. Micro claws are also limited to very rough surfaces such as brick and stone, but they can not function on smooth surfaces such as glass or painted wall. Recently, some progress has been made in locomotion against various types of surfaces with different roughness conditions by using an emerging generation of dry bio-inspired adhesive materials[28] comprising fibrillar arrays, which are similar to those used by geckos, spiders, flies and other insects[22–24]. Bio-inspired adhesive micro/nano-scale fibrillar structures provide high adhesion capacity against a great variety of surfaces at high reliability levels. Selfcleaning is an appealing feature of the fibrillar (inspired by the gecko-foot) adhesion mechanism[25–27]. Various locomotion mechanisms could benefit from the introduction of bio-inspired adhesives for energy-efficient and versatile locomotion against different surfaces[22,23,29–32]. The pressure applied during contact is an important
Peyvandi et al.: A New Self-Loading Locomotion Mechanism for Wall Climbing Robots Employing Biomimetic Adhesives
factor governing the adhesion capacity developed by bio-inspired adhesives (or traditional pressure-sensitive adhesives) against the surface. In this study, a locomotion mechanism (Fig. 1) was developed for streamlined application of the pressure required to bring the adhesive into intimate contact with surfaces of different inclinations and roughness conditions. This mechanism enables effective use of bio-inspired adhesives (as well as traditional pressure-sensitive adhesives) which offer desired qualities such as energy-efficient separation from the surface via peeling[33], ability to adhere to different surfaces, thermal stability[34], and self-cleaning attributes[26,27].
Fig. 1 The locomotion system with bio-inspired adhesives climbing a wall.
2 Mechanism of pressure application upon contact The contacting surfaces of plates connected to wheels are coated with peelable bio-inspired adhesives. These adhesives require application of a minimum pressure upon contact in order to effectively adhere to the surfaces of different types and roughness conditions. The approach adopted here uses the adhesion capacity of two (first group) of the wheels that have already adhered to the surface in order to apply pressure to the other two (second group of) wheels as they establish contact with the surface during locomotion. The first group of wheels would then peel off the surface, and the adhesion capacity of the second group would be used to apply pressure to them as they establish new contacts with the surface. This sequence of events would be repeated in the course of locomotion. The pressure applied to each group of wheels upon contact is equilibrated by the ten-
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sion generated in the other group of wheels, and it does not depend upon surface inclination and gravity. This enables the system to traverse the surfaces of different inclinations (e.g., climb walls). A wheel with two rigid plates (coated with bio-inspired fibrillar adhesive) is shown in Fig. 2. This wheel is made of an elastomer, and the geometry and elastic modulus of the wheel are selected for application of the required contact pressure during locomotion. The wheels in each of the two groups noted above are perpendicular to the wheels in other groups (i.e., the two groups of wheels have 90 degrees rotational phase difference). The difference between the length and width of rectangular wheels is thus the cause of pressure application on a group of wheels establishing contact with the surface during locomotion. In each elastomeric wheel (component 3 in Fig. 2), the contacting surface is that of a rigid plate (component 2 in Fig. 2) that is attached to the wheel via a hinge incorporating a rotational spring (component 5 in Fig. 2). The contacting surface of the plate is coated with a peelable bio-inspired (fibrillar) adhesive (component 1 in Fig. 2). As each plate established contact with the surface, the rotational spring allows it maintain contact with the surface as the wheel undergoes 90 degrees rotation. Afterwards, the plate peel off the surface during another 90 degrees of rotation, and the rotational spring returns it to its original position after it is peeled off the surface. Component 4 in Fig. 2 is a shaft that connects an axle to the wheel. 1
2
2(a+b)
4
2
1 t 3
5
3 2a 2
1
1
2 (a)
(b)
Fig. 2 Wheel (leg) components. (a) Front view; (b) side view.
3 Wheel (leg) design Each wheel in the locomotion mechanism contacts the surface (via plates coated with bio-inspired adhesive) with either its short face (with length 2a) or its long face (with length 2b) facing the surface (Fig. 3). Stiffness of the wheel (under loads normal to the surface applied via axle at mid-height) is a factor in determining the pressure applied upon contact for adherence to the surface.
Journal of Bionic Engineering (2013) Vol.10 No.1
14
When the short side (width) of a wheel contacts the surface, this stiffness, K1 can be written as
Eat K1 = , b
(1)
where E is the elastic modulus of the wheel material, a and b are half the width and length of wheel, respectively, and t is the thickness of wheel. When the long side (length) of a wheel contacts the surface, the stiffness, K2 can be written as
Ebt K2 = , a
F1 = K1δ1 , F2 = K 2δ 2 , F3 = K 3δ 3 , F4 = K 4δ 4 ,
(4)
where δ1, δ2, δ3 and δ4 are the deformations of wheels 1, 2, 3 and 4, respectively, normal to the contact surface over the distance from axle to contact surface. With wheels of similar geometric and material characteristics, and neglecting the gravity effects, the configuration of Fig. 4 produces forces with equal absolute values (|F1|=|F2|=|F3|=|F4|). F2
F3
(2) F1 F4
Fig. 4 Schematic view of forces applied to the four wheels in a particular step during locomotion. Fig. 3 Schematic view of wheel with its dimensions.
Fig. 4 shows the orientations of the wheels in locomotion system. Fig. 4 also shows the forces applied to the wheels in a particular step during locomotion; neglecting the gravity forces would produce similar forces in horizontal, vertical or other configurations of the locomotion system. The applied forces are tensile in the case of wheels with their longer side (length) normal to the surface and they are compressive in the case of wheels with their shorter side (width) normal to the surface. These forces are applied via axles. The wheels receiving compressive forces are those just contacting the surface, and the compressive force generates the pressure required for adhering to the surface via adhesives (bio-inspired or pressure sensitive adhesives). The wheels receiving tensile forces are those that have already adhered to the surface, and their adhesion capacity is used to balance the compressive force applied on newly contacting wheels. The tensile and compressive forces shown in Fig. 4 should balance each other F1 + F3 = F2 + F4 .
(3)
The force developed in each wheel is equal to the product of the wheel stiffness and the wheel deformation in the direction of applied force
Since wheels 1 and 3, and also wheels 2 and 4 act similarly, this discussion focuses on wheels 1 and 2. For these two wheels, ⎛ Eat ⎞ ⎛ Ebt ⎞ K1δ1 = K 2δ 2 ⇒ ⎜ ⎟ δ1 = ⎜ ⎟δ2 . ⎝ b ⎠ ⎝ a ⎠
(5)
Hence,
δ1 b 2 = . δ 2 a2
(6)
Wheels 1 and 2, which are perpendicular to each other, undergo deflections δ1 and δ2 in order to overcome the difference between the distances of their axel from contact surface, that is ∆ = b−a. Hence,
δ1 + δ 2 = Δ ,
(7)
where δ1 and δ2 are expressed as absolute values. The above expressions enable derivation of one dimension of the rectangular wheel (e.g., half the width, b) in terms of its other dimension (e.g., half the length, a) and elastic modulus (E) in order to apply a targeted compressive force (F2) required for adhering to the bio-inspired adhesive to the contact surface, as described below. Eqs. (6) and (7) indicate (using the notation β = b2/a2)
Peyvandi et al.: A New Self-Loading Locomotion Mechanism for Wall Climbing Robots Employing Biomimetic Adhesives
δ1 =
β (b − a) , (1 + β )
(8)
δ2 =
(b − a ) . (1 + β )
(9)
The above equations can be used to derive (b) in terms of (a) and elastic modulus. This design requires the definition of gravity forces, which have been neglected so far. A viable design, however, would require consideration of gravity forces because the effects of gravity forces depend upon surface inclination, mass of the system, and the distance from the center of gravity of the mass to surface. At a critical point during locomotion, two of the wheels are adhered to the surface. These two wheels should be able to resist the tensile and shear forces applied under the combined effects of gravity and the balancing action of wheels described above. This requirement combined with the shear and tensile adhesion capacities of the bio-inspired adhesives would govern the determination of the total contact area of each wheel. This contact area is actually that of a plate connected to the wheel, which is coated with bio-inspired adhesive. Fig. 2 presents the plate geometry; its length is equal to 2(a+b) and its width is equal to the wheel thickness.
15
180-degree rotation of the wheel uses the adhesion capacity of two in-phase wheels to apply pressure on the other two wheels (see Fig. 4). The forces in Fig. 4 are developed due to the phase difference between rotational angles of rectangular wheels connected to a rigid body via axles. The rotational phase difference generates height difference from the axle of each wheel to the contact surface. A more detailed illustration of the operation of one wheel in the locomotion mechanism of Fig. 1 is presented in Fig. 5. The wheel undergoes the four sequential steps shown in Fig. 5 as it undergoes 360 degrees rotation. The rotation of the hinged rigid plate (2a) is enabled by a torsional spring introduced at the hinge location (component 6a in Fig. 5). During the rotation of the wheel, the hinge incorporating the torsional spring is key to maintaining the adhered status of the plate (component 2a in Fig. 5) after the application of pre-load pressure as the wheel undergoes 90 degrees rotation before it peels off the surface as the next hinged plate (component 2b in Fig. 5) establishes contact and receives the pre-load pressure.
4 Kinematics of locomotion Referring to the Fig. 1, each wheel comprises a flexible (elastomeric) rectangular body (component 3 in Fig. 2), with different parts attached to it. These parts include two side plates (component 2 in Fig. 2), which are covered with adhesives (preferably bio-inspired fibrillar adhesives, or pressure-sensitive adhesives) (component 1 in Fig. 2). Two diagonally oriented wheels (see Fig. 1), which rotate around its axis (component 4 in Fig. 2), are in phase (i.e., have the same orientation), and the other two are 90 degrees out of phase with respect to them. The side plates at their attachment locations incorporate torsional springs (component 5 in Fig. 2) which restore their original inclinations after the plate peels off the surface in the course of wheel rotation. Each wheel has two rigid plates, each of which stays in contact with the surface over a rotation angle of 180 degrees. The use of solid plates improves the uniformity of pressure applied to the contact area. Upon separation, the torsional spring (component 5 in Fig. 2) restores the original inclination of the rigid plate. Each
Fig. 5 The sequential steps involved in the rotation of a wheel.
In step 1 (in Fig. 5), plate (2a) has established contact, and received the pre-load pressure required for adhering to the surface. In step 2, the plate has adhered to the surface, and its adhesion capacity is used to apply pre-load pressure to other wheels which are out of phase with respect to it. Plate (2a) remains in contact with the
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Journal of Bionic Engineering (2013) Vol.10 No.1
surface throughout steps 1 and 2. During transformation from step 2 to step 3, plate (2a) separates (peels off) from the surface, and the hinge (6a) incorporating torsional spring returns to the rest position of the torsional spring and brings plate (2a) into its rest position. In step 3, plate (2b) assumes the position of plate (2a) in step 1. In transition from step 3 to step 4, plate (2b) and hinge (6b) play the roles of plate (2a) and hinge (6a) in transition from step 1 to step 2. After step 4, the wheel configuration returns to step 1 because of incorporating torsional spring 6b which wants to return back to its rest position, and the four steps shown in Fig. 5 will be repeated.
The wheels were designed based on the theoretical work presented earlier and were fabricated by casting in molds (Fig. 7a). The side plates at their attachment locations (pins shown in Fig. 7a) incorporate torsional springs (Fig. 7b) which restore the original inclinations of plates after the contact with the surface is lost in the course of wheel rotation (locomotion). Fig. 8 shows two side views of the rectangular wheel with side plates. The side plates and the inclusions in polyurethane wheel were made of aluminum.
5 Experimental validation of the locomotion mechanism Self-loading locomotion mechanism employing bio-inspired adhesives was developed and evaluated. The vehicle embodying the self-loading locomotion mechanismis is 4.5 cm wide and 12.0 cm long[25]. This system has two axles accommodating a total of four wheel-legs. Both axles are driven by a single motor. A rack and pinion steering mechanism pivots the front wheel-legs. The rack and pinion system comprises a pair of gears which convert rotational motion into linear motion. The “pinion” engages teeth on a linear “gear” bar known as the “rack”; rotational motion applied to the pinion causes the rack to move, thereby this action could transfer to the front wheel. The electronics drive system and batteries are contained within the system, and its total weight (including wheels weight) is 130 grams. Fig. 6 shows the details of a rectangular wheel and its side plates. ST-3040 Polyurethane (BJB Enterprise, Inc.) was used for production of the rectangular wheels. This polyurethane has a tensile strength of 5.27 MPa, an elastic modulus of 0.69 MPa, and a hardness of 42 A.
Fig. 6 Geometry detailing of the new rectangular wheel.
Fig. 7 Wheel production and components. (a) Molds used for casting the elastomeric body of wheels; (b) torsional springs used at the pin location of side plates on elastomeric wheels.
Fig. 8 Side views of wheels comprising an elastomeric rectangular body and aluminum components. (a) Back view; (b) front view.
The locomotion mechanism incorporating four rectangular wheels is shown in Fig. 1 on a vertical glass surfaces. The side plates of wheels were covered with bio-inspired adhesives. These adhesives were fibrillar array, comprising fibrils 20 μm in length and 20 μm in diameter (Fig. 9). Tension and shear adhesion capacities of 1 cm × 1 cm specimens of fibrillar arrays which used in locomotion mechanism were measured against glass slides. The experimental was performed on three different samples. These substrates were sonicated in distilled water for 15 minutes, and then blown dried with N2 gas. A preload pressure of 5 kPa (5 N on 1 cm × 1 cm contacted area) was applied to establish adhesion prior to the performance of tension and shear adhesion tests. Based on the adhesion capacity provided by fibrillar array and locomotion system weight, the required bio-inspired adhesive (fibrillar array) was calculated and put on the bottom of each wheels. Developing fibrillar array could provide 25 kPa and 15 kPa shear and tensile adhesion capacity, respectively, against glass (Fig. 10).
Peyvandi et al.: A New Self-Loading Locomotion Mechanism for Wall Climbing Robots Employing Biomimetic Adhesives
Bio-inspired adhesive arrays with 1 cm × 5 cm planar dimensions were placed on the bottom of each plate. The system was evaluated by determining its ability to climb a vertical glass surface (Fig. 1). The locomotion system ascended the vertical surface about 90 cm at a speed of 4 cm·s−1 without falling.
17
can provide unmanned (air or ground) vehicles with versatile mobility in difficult terrain and against inclined or vertical surfaces.
Acknowledgments The authors acknowledge the support of the U.S. Air Force (Contract FA8651-07-C-0092) for the project.
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6 Conclusion A new locomotion mechanism is presented, with wheels employing bio-inspired adhesives for operation against surfaces of different inclination and roughness conditions. This mechanism enables movement on vertical surfaces. The new locomotion mechanism provides the inherent ability to apply pressure on adhesives as they establish contact with the surface, without relying on gravity, in order to effectively adhere to various surfaces of different inclinations. Some of the wheels in this locomotion-mechanism have rotational phase difference with respect to the other wheels. At each moment, the in-phase wheels have established adhesion with the surface, and are used to apply pressure to the other wheels as they contact the surface. In order to validate this self-loading locomotion mechanism, prototype system was designed and fabricated using bio-inspired adhesives and was tested on vertical glass surfaces. The system ascended the vertical surface at a speed of 4 cm·s−1 without falling. This locomotion mechanism
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