1 Introduction

As the core unit of energy conversion, motors with excellent performance usually play a crucial role in many scientific and engineering fields [1,2,3]. Generally, positioning accuracy, working stroke, loading capability, operating velocity, motion resolution, and overall dimensions are the most important performance criteria for high-end motors [4, 5]. Traditional motors, such as internal-combustion engines, electromagnetic motors, hydraulic motors, and pneumatic motors, exhibit many favorable characteristics, including large torque, long working stroke, and high stiffness. However, they can hardly overcome the defects such as oversize volume, accumulation error, motion loss, and wind up [6, 7]. With the rapid rise of technical requirements, traditional motors have been unable to satisfy the modern scientific and engineering fields [6, 7]. The development of next-generation motors with more excellent characteristics has become one of the most active research hotspots [8,9,10,11,12].

Piezoelectric motors driven by piezoelectric materials are developed as time advances. Piezoelectric materials are a kind of smart functional materials which work with the piezoelectric effects including direct piezoelectric effect and inverse piezoelectric effect [13, 14]. The direct piezoelectric effect refers to when deformation occurs under the action of external force, the piezoelectric materials can produce electric charges at the two electrodes [15,16,17]. On the contrary, the inverse piezoelectric effect is that when we supply electricity to the two electrodes, the piezoelectric materials can generate deformations [15,16,17]. In general, the direct piezoelectric effect enables the piezoelectric materials to be excellent sensing elements, and the inverse piezoelectric effect can be used to develop precision motors. As actuation materials, the piezoelectric materials mainly exhibit the following advantages: (1) ultra-high accuracy, up to sub-nanometer scale; (2) super-fast response, up to microsecond level; (3) large output force and high mechanical stiffness; (4) no magnetic field interference, no magnetic field generation, and unaffected by the external magnetic field; (5) strong adaptability, applicable for the vacuum, and low-temperature environments; (6) no intermediate transmission, no moving pair clearance, and no lubrication required; (7) high electromechanical conversion rate and high energy density; (8) diverse structures, flexible design and easy miniaturization [15,16,17]. Therefore, both in terms of structures and functions, the piezoelectric materials are excellent actuation components for a new generation of motors.

In recent decades, numerous types of piezoelectric motors have been developed, which have been widely used in the precision drive systems, such as the manipulation of biological specimens, optical element alignment, semiconductor equipment, insect-scaled robots, and micro-positioning stages [15,16,17,18,19]. Meanwhile, strenuous efforts have been made to address the shortcomings of a small strain of piezoelectric materials [18, 19]. First, the piezo-stack with a multilayer structure combined the small strains from many single-layer units into a long output displacement [20, 21]. The work range of piezo-stack motors could reach tens of micrometers [22, 23]. Second, various amplification mechanisms were designed to enlarge the displacement of piezoelectric materials, such as the lever mechanism [24, 25], bridge mechanism [26, 27], Scott-Russell mechanism [28, 29], and bimorph mechanism [30, 31]. By virtue of various amplification mechanisms, the work range of piezoelectric motors could reach hundreds of micrometers [32, 33]. However, this was still insufficient in many applications. Therefore, researchers created different bionic stepping piezoelectric motors by imitating the walking manner of some typical animals [34,35,36]. According to the practical requirements, the bionic stepping piezoelectric motors were able to accumulate the small displacements of piezoelectric materials and generate a sufficient traveling stroke step by step. With the stepping motion principles, the piezoelectric motors are completely liberated from the small displacement and preserve the main advantages of piezoelectric materials, concurrently. The work range of the bionic stepping piezoelectric motors can reach a millimeter scale or even without limit [34,35,36].

This work proposes a comprehensive review of bionic stepping piezoelectric motors with cross-scale output performance. The review is outlined in form of rotary piezoelectric motors, while the overall contents cover both the linear motors and rotary motors. Correspondingly, the contents of the review are organized as follows: in Sect. 2, the bionic stepping piezoelectric motors are classified into inchworm motors, seal motors, and inertia motors. In Sect. 3, the classifications, configurations, and working principles of the inchworm piezoelectric motors are introduced. In Sect. 4, we elaborate the classifications, configurations, and working principles of the seal piezoelectric motors. In Sect. 5, the classifications, configurations, and working principles of the inertia piezoelectric motors are presented. The characteristics of the three types of bionic stepping piezoelectric motors are analyzed in Sect. 6. Conclusions of the work are reported in Sect. 7.

2 Overview of the Bionic Stepping Piezoelectric Motors

Bionic stepping piezoelectric motors, just as its name implies, imitate some animals’ typical behavioral manners to accumulate the small displacements of piezoelectric materials to generate sufficient working stroke step by step. Generally, a bionic stepping piezoelectric motor contains a feeding module, clamping module, and other key components [34,35,36]. The feeding module is utilized to produce driving displacements of the rotor while the clamping module is employed to clamp/unclamp the rotor to/from the stator at the appropriate time [34,35,36]. With the sequential coordination of the feeding module and clamping module, the bionic stepping piezoelectric motor can drive the rotor to output large angular displacements step by step.

It is universally acknowledged that the motors can be called bionic stepping piezoelectric motors provided the feeding module is driven by piezoelectric materials [34,35,36]. The outputs of the piezoelectric materials are linear displacements including the longitudinal strains, transversal strains, and shear strains, which can all be used to drive the motor. In order to achieve angular displacements of piezoelectric motors, considerable efforts have been made by different researchers. For example, flexure hinges, revolute pairs, and other methods are utilized to transform linear displacements into angular displacements [37,38,39,40,41,42]. Flexure hinges are a kind of deformable mechanism to guide movements, which consist of flexible parts and rigid parts. The flexible parts with small stiffness and the rigid parts with large stiffness are designed and machined from a single piece of material [37,38,39,40,41,42]. With the given deformations and constraints of flexible parts, the rigid parts can move at certain degrees of freedom. Owing to the advantages of compliant and repeatable motions, compact structures, small inertial mass, no backlash, and friction, the flexure hinges are widely utilized in piezoelectric motors, especially in stepping piezoelectric motors [37,38,39,40,41,42]. Furthermore, with the designed flexure hinges mechanisms, we can not only obtain the angular displacements but also multiply and enlarge the small deformations of piezoelectric materials [40,41,42].

Many clamping methods are reported by the researchers, such as the deformation clamp [43, 44], electromagnet clamp [45, 46], inertia clamp [47, 48], and wedge clamp [49, 50]. The deformation clamp utilizes the deformation of the clamping component to tension rotor into the bearing of stator. With the adhesion force of an electromagnet, the electromagnet clamp can clamp the rotor onto the stator. The inertia clamp presses the rotor onto the stator with the inertial force generated by a mass block during acceleration. The wedge clamp can clamp the rotor onto the stator with the self-lock effect between a wedge block pair. Since almost all the stepping piezoelectric motors use frictional force to maintain the output thrust, the clamping force determines the capacity of the stepping piezoelectric motors [43,44,45,46]. Moreover, because of the contact and separation during the clamping process, the clamping module also influences the stepping piezoelectric motors from the vibration, noise, accuracy, and so on [47,48,49,50].

In terms of the main structure modules, as shown in Fig. 1, the bionic stepping piezoelectric motors are classified into inchworm motors [51,52,53], seal motors [54,55,56], and inertia motors [57,58,59,60]. Each type of these stepping motors can be further divided into walker type, pusher type, and hybrid type. All the bionic stepping piezoelectric motors have specific configurations, working principles, and characteristics. A suitable type of piezoelectric motor can be selected according to the actual demand.

Fig. 1
figure 1

Classifications of bionic stepping piezoelectric motors

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3 Inchworm Piezoelectric Motors

3.1 Inchworm Motion Principle

The inchworm is an arthropod with a slender body and many pairs of feet. The body is flexible and bendable. The feet are on both ends of the body, which are named as fore feet and hind feet respectively. As shown in Fig. 2, the crawling manner of the inchworm is a typical stepping motion. The process can be divided into different steps: first, the inchworm grips on the branch with the fore feet and hind feet; second, it releases the fore feet from the branch; third, it straightens the body and pushes forward the fore feet; fourth, it grips on the branch again with the fore feet; fifth, it releases the hind feet from the branch; sixth, it bends the body again and pulls forward the hind feet; lastly, it grips on the branch again with the hind feet. After the above process, the inchworm moves forward one step on the branch and returns back to the initial status (the first step). Obviously, if the above process is repeated time after time, the inchworm can crawl with a long distance on the branch.

Fig. 2
figure 2

Stepping motion of the inchworm

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Imitating the crawling manner of the inchworm, researchers created the inchworm-type bionic stepping piezoelectric motors. As Fig. 3 shows, the inchworm piezoelectric motors are mainly composed of a feeding module to imitate the bendable body and two clamping modules to imitate the fore feet and the hind feet [51,52,53]. The feeding module is used to generate the driving angular displacements and the clamping modules are employed to clamp or unclamp the rotor at the right time interval. According to the relative position relationships among the feeding module and the clamping modules, the inchworm piezoelectric motors can be classified into three types, which are named walker inchworm motors (see Fig. 3a), pusher inchworm motors (see Fig. 3b), and hybrid inchworm motors (see Fig. 3c), respectively [51,52,53]. The basic structures and working principles of these three types of inchworm piezoelectric motors are elaborated in the following discussion.

Fig. 3
figure 3

Working principles of the inchworm motors. a Walker inchworm motor; b pusher inchworm motor; c hybrid inchworm motor

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3.2 Walker Inchworm Motor

The walker inchworm motor consists of one feeding module and two clamping modules. As shown in Fig. 3a, the feeding module and two clamping modules are all installed on the rotor, which rotate with the rotor during the operation process of the walker inchworm motor [51,52,53]. The stepping motion process of the walker inchworm motor is shown in Fig. 3a from Step (0) to Step (7), which are described as follows:

  1. (1)

    The initial status of the walker inchworm motor.

  2. (2)

    The clamping module at the right side runs and clamps the feeding module to the stator.

  3. (3)

    The feeding module runs and pushes the upper clamping module and the rotor to rotate by an angle θ, anticlockwise.

  4. (4)

    The upper clamping module runs and clamps the rotor to the stator.

  5. (5)

    The clamping module at the right side is reset and releases the feeding module from the stator.

  6. (6)

    The feeding module is reset and pulls the clamping module at the right side to rotate anticlockwise.

  7. (7)

    The clamping module at the right side runs again and clamps the feeding module to the stator again.

  8. (8)

    The upper clamping module is reset and releases the rotor from the stator. The walker inchworm motor returns back to the status in Step (1).

After the above operations from Step (1) to Step (7), the walker inchworm motor drives the rotor by an angle θ anticlockwise and returns back to the status in Step (1). If the above operations are repeated time by time, the walker inchworm motor can continually output angular displacements step by step. In addition, the backward rotary motions can be generated by adjusting the working sequences of the feeding module and two clamping modules.

3.3 Pusher Inchworm Motor

The pusher inchworm motor consists of one feeding module and two clamping modules. As shown in Fig. 3b, the feeding module and two clamping modules are all installed on the stator and do not rotate with the rotor during the operation process of the pusher inchworm motor [51,52,53]. The stepping motion process of the pusher inchworm motor is shown in Fig. 3b from Step (0) to Step (7), which are described as follows:

  1. (1)

    The initial status of the pusher inchworm motor.

  2. (2)

    The upper clamping module runs and clamps the rotor to the feeding module.

  3. (3)

    The feeding module runs and pushes the upper clamping module and the rotor to rotate by an angle θ, anticlockwise.

  4. (4)

    The clamping module at the right side runs and clamps the rotor to the stator.

  5. (5)

    The upper clamping module is reset and releases the rotor from the feeding module.

  6. (6)

    The feeding module is reset and pulls the upper clamping module to rotate clockwise.

  7. (7)

    The upper clamping module runs again and clamps the rotor to the feeding module again.

  8. (8)

    The clamping module at the right side is reset and releases the rotor from the stator. The pusher inchworm motor returns back to the status in Step (1).

After the above operations from Step (1) to Step (7), the pusher inchworm motor drives the rotor by an angle θ anticlockwise and returns back to the status in Step (1). If the above operations are repeated time by time, the pusher inchworm motor can continually output angular displacements step by step. In addition, the backward rotary motions can be generated by adjusting the working sequences of the feeding module and two clamping modules.

3.4 Hybrid Inchworm Motor

The hybrid inchworm motor also consists of one feeding module and two clamping modules. As shown in Fig. 3c, the feeding module is installed on the rotor while the two clamping modules are installed on the stator [51,52,53]. Certainly, the positions of the feeding module and two clamping modules can also be exchanged. The module which is installed on the rotor rotates with it during the operation process of the hybrid inchworm motor and the module installed on the stator is relative static with the stator [51,52,53]. The stepping motion process of the hybrid inchworm motor is shown in Fig. 3c from Step (0) to Step (7), which are described as follows:

  1. (1)

    The initial status of the hybrid inchworm motor.

  2. (2)

    The clamping module at the right side runs and clamps the feeding module to the stator.

  3. (3)

    The feeding module runs and pushes the rotor to rotate by an angle θ, anticlockwise.

  4. (4)

    The lower clamping module runs and clamps the rotor to the stator.

  5. (5)

    The clamping module at the right side is reset and releases the feeding module from the stator.

  6. (6)

    The feeding module is reset and pulls the right part to rotate anticlockwise.

  7. (7)

    The clamping module at the right side runs again and clamps the feeding module to the stator again.

  8. (8)

    The lower clamping module is reset and releases the rotor from the stator. The hybrid inchworm motor returns back to the status in Step (1).

After the above operations from Step (1) to Step (7), the hybrid inchworm motor drives the rotor by an angle θ anticlockwise and returns back to the status in Step (1). If the above operations are repeated time by time, the hybrid inchworm motor can continually output angular displacements step by step. In addition, the backward rotary motions can be generated by adjusting the working sequences of the feeding module and two clamping modules.

4 Seal Piezoelectric Motors

4.1 Seal Motion Principle

The seal is a marine mammal with a contractible body and two pairs of feet. The body is elastic and can expand and contract. The hind feet have degenerated into fins without walking ability, while the fore feet can bend and assist crawling. As shown in Fig. 4, the crawling manner of the seal is another type of stepping motion, which is different from the inchworm type. The process is as follows: first, the seal is on the beach with the cumbersome body; second, it grips on the ground with the fore feet; third, it contracts the body and pulls forward the tail and the hind feet; fourthly, it releases the fore feet from the ground; lastly, it expands the body and pushes forward the fore feet and the head. After the above process, the seal moves forward one step on the beach and returns back to the initial status (the first step). Obviously, if the above process is repeated time after time, the seal can crawl with a long distance on the beach.

Fig. 4
figure 4

Stepping motion of the seal

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Inspired by the crawling mode of the seal, the seal-type bionic stepping piezoelectric motors are developed. As shown in Fig. 5, the seal piezoelectric motors are mainly composed of a feeding module to imitate the contractible body, a clamping module to imitate the fore feet with the crawling ability and a locking component to imitate the hind feet without crawling ability [54,55,56]. The feeding module is used to generate the driving angular displacements and the clamping module is employed to clamp or unclamp the rotor at the right time interval. The locking component is utilized to maintain the output thrust during the unclamping time interval of the clamping module. According to the relative position relationships among the feeding module, clamping module, and locking component, the seal piezoelectric motors can further be classified into three types, which are named walker seal motors (see Fig. 5a), pusher seal motors (see Fig. 5b), and hybrid seal motors (see Fig. 5c), respectively [54,55,56]. The basic structures and working principles of these three types of seal piezoelectric motors are elaborated in the following discussion.

Fig. 5
figure 5

Working principles of the seal motors. a Walker seal motor; b pusher seal motor; c hybrid seal motor

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4.2 Walker Seal Motor

The walker seal motor consists of one feeding module, one clamping module, and one locking component. As shown in Fig. 5a, the feeding module, the clamping module, and the locking component are all installed on the rotor and rotate with the rotor during the operation process of the walker seal motor [54,55,56]. The stepping motion process of the walker seal motor is shown in Fig. 5a from Step (0) to Step (4), which are described as follows:

  1. (1)

    The initial status of the walker seal motor.

  2. (2)

    The clamping module runs and clamps the feeding module to the stator.

  3. (3)

    The feeding module runs and pushes the locking component and the rotor to rotate by an angle θ, anticlockwise.

  4. (4)

    The clamping module is reset and releases the feeding module from the stator.

  5. (5)

    The feeding module is reset and pulls the clamping module to rotate anticlockwise and the walker seal motor returns back to the status in Step (0).

After the above operations from Step (0) to Step (4), the walker seal motor drives the rotor by an angle θ anticlockwise and returns back to the status in Step (0). If the above operations are repeated time by time, the walker seal motor can continually output angular displacements step by step. The locking component can maintain the output thrust for the walker seal motor throughout the process. In addition, the backward rotary motions can be generated by adjusting the working sequences of the feeding module and the clamping module.

4.3 Pusher Seal Motor

The pusher seal motor consists of one feeding module, one clamping module, and one locking component. As shown in Fig. 5b, the feeding module, the clamping module, and the locking component are all installed on the stator and do not rotate with the rotor during the operation process of the pusher seal motor [54,55,56]. The stepping motion process of the pusher seal motor is shown in Fig. 5b from Step (0) to Step (4), which are described as follows:

  1. (1)

    The initial status of the pusher seal motor.

  2. (2)

    The clamping module runs and clamps the rotor to the feeding module.

  3. (3)

    The feeding module runs and pushes the clamping module and the rotor to rotate by an angle θ, anticlockwise.

  4. (4)

    The clamping module is reset and releases the rotor from the feeding module.

  5. (5)

    The feeding module is reset and pulls the clamping module to rotate clockwise and the pusher seal motor returns back to the status in Step (0).

After the above operations from Step (0) to Step (4), the pusher seal motor drives the rotor by an angle θ anticlockwise and returns back to the status in Step (0). If the above operations are repeated time by time, the pusher seal motor can continually output angular displacements step by step. The locking component can maintain the output thrust for the pusher seal motor throughout the process. In addition, the backward rotary motions can be generated by adjusting the working sequences of the feeding module and the clamping module.

4.4 Hybrid Seal Motor

The hybrid seal motor also consists of one feeding module, one clamping module, and one locking component. As shown in Fig. 5c, the feeding module is installed on the rotor while the clamping module and the locking component are both installed on the stator. Certainly, the positions of the feeding module, clamping module, and locking component can be exchanged. The module which is installed on the rotor rotates with the rotor during the operation process of the hybrid seal motor and the module which is installed on the stator is relative static with the stator [54,55,56]. The stepping motion process of the hybrid seal motor is shown in Fig. 5c from Step (0) to Step (4), which are described as follows:

  1. (1)

    The initial status of the hybrid seal motor.

  2. (2)

    The clamping module runs and clamps the feeding module to the stator.

  3. (3)

    The feeding module runs and pushes the rotor to rotate by an angle θ, anticlockwise.

  4. (4)

    The clamping module is reset and releases the feeding module from the stator.

  5. (5)

    The feeding module is reset and pulls the right part to rotate anticlockwise and the hybrid seal motor returns back to the status in Step (0).

After the above operations from Step (0) to Step (4), the hybrid seal motor drives the rotor by an angle θ anticlockwise and returns back to the status in Step (0). If the above operations are repeated time by time, the hybrid seal motor can continually output angular displacements step by step. The locking component can maintain the output thrust for the hybrid seal motor throughout the process. In addition, the backward rotary motions can be generated by adjusting the working sequences of the feeding module and the clamping module.

5 Inertia Piezoelectric Motors

5.1 Inertia Motion Principle

IN nature, there are many examples that animals use inertia to achieve some goals. Dogs use inertia to shake off the water drops on hairs. Another more typical example is that the rhinoceros utilize inertia to assist their parturition. Due to the lack of external pulling force, it is difficult for the rhinoceros to deliver quickly. As shown in Fig. 6, the rhinoceros rotates the body time after time to fling the hip in order to accelerate the parturition process. Under the action of the self-inertia, the cub can be flung out of the birth canal step by step. Finally, the rhinoceros cub is born successfully.

Fig. 6
figure 6

Parturition with inertia force

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Imitating the parturition manner of the rhinoceros, the inertia-type bionic stepping piezoelectric motors are developed. As shown in Fig. 7, the inertia piezoelectric motors are mainly composed of one feeding module, one locking component, and one inertia mass [57,58,59,60]. The feeding module is used to generate the driving angular displacements. The locking component is employed to maintain the output thrust throughout the working process. The inertia mass is utilized to generate the inertia torque to drive the rotor. According to the relative position relationships among the feeding module, the locking component, and the inertia mass, the inertia piezoelectric motors can be classified into three types, which are named walker inertia motors (see Fig. 7a), pusher inertia motors (see Fig. 7b), and hybrid inertia motors (see Fig. 7c), respectively [57,58,59,60]. The basic structures and working principles of the three types of inertia piezoelectric motors are elaborated in the following discussion.

Fig. 7
figure 7

Working principles of the inertia motors. a Walker inertia motor (Impact type motor); b pusher inertia motor (stick–slip type motor); c hybrid inertia motor

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5.2 Walker Inertia Motor

The walker inertia motor, which is usually called impact type motor, consists of one feeding module, one locking component, and one inertia mass. As shown in Fig. 7a, the feeding module, the locking component, and the inertia mass are all installed on the rotor and rotated with the rotor during the operation process of the walker inertia motor [57,58,59,60]. The stepping motion process of the walker inertia motor is shown in Fig. 7a from Step (0) to Step (2), which are described as follows:

  1. (1)

    The initial status of the walker inertia motor.

  2. (2)

    The feeding module runs rapidly. Under the action of self-inertia, the inertia mass stays still and the rotor and the locking component are pushed rapidly to rotate by an angle θ, anticlockwise.

  3. (3)

    The feeding module is reset slowly. Under the action of the locking component, the rotor and the locking component stay still and the inertia mass is pulled slowly to rotate anticlockwise. The walker inertia motor returns back to the status in Step (0).

After the above operations from Step (0) to Step (2), the walker inertia motor drives the rotor by an angle θ anticlockwise and returns back to the status in Step (0). If the above operations are repeated time by time, the walker inertia motor can continually output angular displacements step by step. The locking component can maintain the output thrust for the walker inertia motor throughout the process. In addition, the backward rotary motions can be generated by exchanging the rapid functional step and the slow functional step of the feeding module.

5.3 Pusher Inertia Motor

The pusher inertia motor, which is usually called stick–slip type motor, consists of one feeding module, one locking component, and one inertia mass. As shown in Fig. 7b, the feeding module, the locking component, and the inertia mass are all installed on the stator and do not rotate with the rotor during the operation process of the pusher inertia motor [57,58,59,60]. The stepping motion process of the pusher inertia motor is shown in Fig. 7b from Step (0) to Step (2), which are described as follows:

  1. (1)

    The initial status of the pusher inertia motor.

  2. (2)

    The feeding module runs slowly. Under the action of the locking component, the rotor and the inertia mass are pushed slowly to rotate by an angle θ, anticlockwise.

  3. (3)

    The feeding module is reset rapidly. Under the action of inertia of the inertia mass, the rotor and inertia mass stay still and the locking component is pulled rapidly to rotate clockwise. The pusher inertia motor returns back to the status in Step (0).

After the above operations from Step (0) to Step (2), the pusher inertia motor drives the rotor by an angle θ anticlockwise and returns back to the status in Step (0). If the above operations are repeated time by time, the pusher inertia motor can continually output angular displacements step by step. The locking component can maintain the output thrust for the pusher inertia motor throughout the process. In addition, the backward rotary motions can be generated by exchanging the rapid functional step and the slow functional step of the feeding module.

5.4 Hybrid Inertia Motor

The hybrid inertia motor also consists of one feeding module, one locking component and one inertia mass. As shown in Fig. 7c, the feeding module and the inertia mass are both installed on the rotor while the locking component is installed on the stator [57,58,59,60]. The positions of the feeding module, locking component, and inertia mass can be exchanged. The module installed on the rotor rotates with the rotor during the operation process of the hybrid inertia motor, while the module installed on the stator is relative static with the stator. The stepping motion process of the hybrid inertia motor is shown in Fig. 7c from Step (0) to Step (2), which are described as follows:

  1. (1)

    The initial status of the hybrid inertia motor.

  2. (2)

    The feeding module runs rapidly. Under the action of self-inertia, inertia mass stays still and the rotor is pushed rapidly to rotate by an angle θ, anticlockwise.

  3. (3)

    The feeding module is reset slowly. Under the action of the locking component, the rotor stays still and the inertia mass is pulled slowly to rotate anticlockwise. The hybrid inertia motor returns back to the status in Step (0).

After the above operations from Step (0) to Step (2), the hybrid inertia motor drives the rotor by an angle θ anticlockwise and returns back to the status in Step (0). If the above operations are repeated time by time, the hybrid inertia motor can continually output angular displacements step by step. The locking component can maintain the output thrust for the hybrid inertia motor throughout the process. In addition, the backward rotary motions can be generated by exchanging the rapid functional step and the slow functional step of the feeding module.

6 Characteristics of Stepping Piezoelectric Motors

By virtue of the bionic stepping principles, the piezoelectric motor can accumulate small displacements from the piezoelectric materials step by step and generate a long-range working stroke. Consequently, the piezoelectric motors completely liberate themselves from the small deformations and inherit the main advantages of piezoelectric materials as well. The work range of stepping piezoelectric motors can reach several radians, or even without limit, and the resolution can reach microradian. The inchworm motors, seal motors, and inertia motors are the three types of most commonly used bionic stepping piezoelectric motors. In Table 1, the performance data of typical stepping piezoelectric motors are summarized.

Table 1 Performance of stepping piezoelectric motors
Full size table

In terms of the configurations, the inchworm motor contains one feeding module and two clamping modules. If one of these two clamping modules is replaced by a locking component, the inchworm motor can be transformed into a seal motor. Therefore, the seal motor contains one feeding module, one clamping module, and one locking component. If the other clamping module is further replaced by an inertia mass, the seal motor is transformed into an inertia motor. Therefore, the inertia motor contains one feeding module, one locking component, and one inertia mass. These are the transformational relations among the three types of bionic stepping piezoelectric motors. Moreover, the characteristics of the three types of motors are compared in Table 2.

Table 2 Characteristics of stepping piezoelectric motors
Full size table

The clamping module can provide a large clamping force during the stepping motion. However, it has a complicated structure and requires additional control and enough time response during the clamping process. Moreover, the contact and separation of the clamping module cause vibrations and motion errors in the rotor. Therefore, the inchworm motors composed of one feeding module and two clamping modules show large load capacity, whereas they have oversized structure, large oscillation, slow velocity, and complicated control system [61,62,63,64,65,66,67,68,69,70,71,72]. In contrast, the inertia motors, which are composed of one feeding module, one locking component, and one inertia mass, have compact structure, small oscillation, fast velocity, and a simple control system, while the load capacity is small [73,74,75,76,77,78,79,80,81,82]. In addition, due to the intrinsic limitation of the inertia principle, there is rollback motion at every step of the inertia motor. Large preload force of the rotor and the large mass of the inertia block can reduce the rollback motion and increase the load capacity of the inertia motor. As for the seal motors composed of one feeding module, one clamping module and one locking component, the properties of the structure, oscillation, and velocity as well as the complexity of control system are at an intermediate level between those of the inchworm motors and inertia motors [83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100].

According to the relative position relationships among the main structure modules, each of the inchworm motor, seal motor, and inertia motor can be classified into walker type, pusher type, and hybrid type. For the walker motor, all the functional modules are installed on the rotor. Namely, the walker motor possesses a stator with simple structures and a rotor with complex structures [61,62,63,64,65,66,67,68,69,70,71,72]. For the pusher motor, all the functional modules are installed on the stator. Therefore, the pusher motor has a stator with a complex structure and a rotor with a simple structure [73,74,75,76,77,78,79,80,81,82]. For the hybrid motor, the functional modules are installed on both the stator and the rotor. Therefore, the hybrid motor possesses a moderate stator and a moderate rotor [73,74,75,76,77,78,79,80,81,82]. Generally, the walker motor has large capacity. Because the long radius of the big volume rotor contributes to the large driving torque [61,62,63,64,65,66,67,68]. If the capability to output many revolutions of the motor is required, the pusher motor is the optimal choice, as there is no electric module on the rotor. In addition, the pusher motor is provided with a high speed due to the light weight of the rotor [61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82]. Clearly, the characteristics of the hybrid motor are at an intermediate level between those of the walker motor and the pusher motor [95,96,97,98,99,100].

7 Conclusions

In this work, the bionic stepping motors driven by piezoelectric materials are comprehensively reviewed. The characteristics of three important bionic stepping piezoelectric motors are elaborated, including the inchworm motors, seal motors, and inertia motors, which all present high motion resolution and long working stroke. The mutual transformation relationships among the three types of motors by replacing certain components are elaborated especially. The inchworm motors composed of one feeding module and two clamping modules show large load capacity, whereas they have oversized structure, large oscillation, slow velocity, and complicated control system. In contrast, the inertia motors, composed of one feeding module, one locking component, and one inertia mass, have a compact structure, small oscillation, fast velocity, and a simple control system, while the load capacity is small. As for the seal motors composed of one feeding module, one clamping module, and one locking component, the properties of the structure, oscillation and velocity, as well as the complexity of the control system are at an intermediate level between those of the inchworm motors and inertia motors. Moreover, each of the inchworm motors, seal motors and inertia motors can further be classified into walker type, pusher type, and hybrid type, according to the relative position relationships among the main structure modules. The walker type possesses large capacity, while its velocity is smaller than the pusher type. The characteristics of the hybrid type are intermediate as compared to the walker type, and pusher type. In summary, the structures, principles, classifications, correlations, and performance of various types of bionic stepping piezoelectric motors are elaborated and reviewed. The work is beneficial for researchers and engineers to investigate the existing piezoelectric motors and to explore novel driving principles and methods for better engineering applications.

Future research directions are suggested as follows:

  1. (1)

    The clamping components need to be improved to reduce the vibration of the rotor during the clamping movement.

  2. (2)

    Structure optimization, lightweight material, and advanced process can profit the compact volume, stable operation, and performance improvement of the stepping piezoelectric motors.

  3. (3)

    It is of significance to develop piezoelectric motors with multiple degrees of freedom and multiple stepping principles.

  4. (4)

    New stepping principles and novel driving methods should continue to be explored to elevate the performance of piezoelectric motors.