1 Introductions

Smart manufacturing is a strong industrial driver for reshaping the current competitive landscape and establishing new market leaders. Manufacturing has evolved to become more automated, computerized, and complex. Smart manufacturing can be defined as a set of technologies that employ a computer-integrated process, high levels of adaptability, rapid design changes, digital information technology, and more flexible technical workforce training [1]. Smart manufacturing allows building of new value-added processes and networks to improve and optimize the flexibility, adaptability, and efficiency of business processes.

Cyber-physical systems (CPS)—a new trend in smart manufacturing-related research—integrates the cyber world and the dynamic physical world by combining computing, communication, and control [2]. The main feature is the integration of cyber-physical systems to enable intersystem communication and self-controlled system operation [3]. Moreover, smart factories integrated with CPS can be easily applied to a big data analytics platform to collect data on industrial processes [4, 5]. This would enable physical entities in smart manufacturing to be controlled and supervised in a safe, efficient, and reliable manner [6].

Additive manufacturing (AM) or three-dimensional (3D) printing is considered as a CPS owing to the interlacing of virtual production with physical production [7]. AM has introduced new production methods to design, manufacture, and distribute to end users. Moreover, AM plays an important role in smart manufacturing owing to its various benefits such as time and material savings, rapid prototyping, high efficiency, and decentralized production [8, 9].

Although AM technologies have experienced substantial growth in recent decades, machining manufacturing (MM) has played a dominant role in manufacturing. AM is highly suitable for green manufacturing owing to its advantages such as material saving and waste minimization [9]. However, it is not relevant to the manufacturing of large-scale products with metals and high-standard surface finishing [10]. In addition, AM has limitations in terms of material use, whereas MM is easy to apply because of the variety of materials available on the market. Finally, metal parts manufactured by AM require additional trimming with computer numerical control (CNC) machines in the case of a high precision finish [11].

Even though manufacturing automation has become extremely popular in the past 30 years, advances in AI and robots will ensure significant development in this field [12, 13]. AI is comparable to the brain in the automation process, with industrial machining robots being the body cells. In future factory automation, robots will play an important role in customizing the production process, including picking and placing, welding, painting, packaging and labeling, palletizing, and product inspection.

Machining robots are expected to significantly change existing production systems for a variety of reasons [14]. Many industrial robots are being utilized in the machining process to increase productivity and reduce labor costs. In general, a typical machining robot system includes a serial robotic arm with a machining tool attached to the end-effector of the robot [15]. Compared to traditional machining systems, these machining robots can easily expand the workspace having additional mobile platforms attached [16]. The rise of machining robots in modern factories is undeniable. In particular, 78% of industrial robot productivity in the market is used in welding and handling operations, of which more than 40% is used in the automotive and metal processing industries [17]. However, these machining robots have diverse applications because the tools mounted on the end-effector easily can be changed for different tasks, such as grinding and welding [18].

The quality of the machining process with robots is mainly governed by the accuracy and stiffness of the robots [19]. There are three types of errors affecting the accuracy of a robot: errors due to the working environment, machining process errors, and robot self-dependent errors [20]. The errors in a robot due to structural deformations of load-transmitting components, links, energy-transforming devices, or wear and nonlinear effects are hardly controllable [13, 20]. However, some of the self-dependent errors in a robot can be compensated for by suitable control or dedicated calibration [21].

The precision reducer is an important component governing the accuracy of the machining robot. High-quality mechanical and electrical parts can be used to improve the accuracy of the robot to obtain the best precision. Among these, precision reducers used in joint actuators contribute significantly to the kinematic and nongeometrical position errors of robots [22].

This paper presents a review of rigid precision reducers of industrial robots for machining. Initially, an overview of the machining robots and their features are introduced. The importance of a precision reducer as a key component of a robot for machining is explored. A cycloid reducer is the best candidate among precision reducers, considering both the structural compliance and kinematic accuracy of the machining robots. Various cycloid reducers and their operating principles are reviewed. The design issues of the cycloid reducer for performance improvement are presented. Additionally, the methodology and analysis for assessing the performance of the cycloid reducers are discussed. Afterward, the machining and fault detection of a cycloid reducer are briefly presented. Finally, other applications of cycloid reducers are introduced.

2 Machining Robot and its Characteristics

Prototypical machining robots—6-or 7-degree-of-freedom (DOF) structures of industrial robotic arms—have been used for various tasks such as milling, grilling, polishing, and cutting. An example of a 6-DOF robotic arm for the milling process is shown in Fig. 1 [23]. In this task, a machining tool is attached to the end-effector of an industrial robot. The tool can be conveniently changed on the spindle attached to the end-effector of the robot to execute other machining tasks [16]. Various studies on machining robots are presented in Table 1 [24].

Fig. 1
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KUKA milling robot [23] (open accessed)

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Table 1 Applications of machining robot in different manufacturing fields [24]
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The machining robot system offers many advantages over conventional CNC machines, as shown in Table 2 [25, 26]. Primarily, the workspace of the machining robot is very large and can be shared owing to the high flexibility of their arms [27]. As a result, complex bulky 3D shapes, such as an aircraft, can be machined directly with the robot. Moreover, a tool path for its smoothness can be further optimized using redundant joint actuators, although trajectory planning is significantly complex compared to conventional CNC. Time and substantial effort are required to train operators who have little or no software knowledge can be saved by using the robot system.

Table 2 Comparison between machining robots and CNC machines
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Operational accuracy and structural stiffness are crucial in machining robots. During processes with negligible machining forces, such as welding or routing, only kinematic position errors need to be considered [28]. Compliance is very important in resisting the structural deformation caused by machining forces during the cutting or milling process [29]. Some methods have been proposed to improve the operational accuracy and structural stiffness of machining robots [21, 29]. The spindle of the robot is directly attached to its fifth joint to reduce the effect of the machining forces, which limits the flexibility and workspace of the robot [16]. Compliance compensation also helps to improve the performance of a machining robot with kinematic position and nongeometrical errors. Nevertheless, the control system of machining robots is extremely expensive and complicated because several high-resolution sensors and tracker-checking systems are required [30].

Choice of proper components in the machining robot is crucial for reducing compliance issues. The ability and performance of robots are influenced by the working environment, accuracy of the robot control system, and robot dependent errors (both kinetics and dynamics) [20]. While factors such as the working environment and control system accuracy can be adjusted during robot operation [21, 22, 28], the robot-dependence errors need to be considered in the robot manufacturing process. Robot-dependence errors include geometrical and nongeometrical errors [20]. Most of the geometrical errors result from the quality of actuators located in the joints of the robot, which is a combination of motors and high-precision reducers [31, 32]. Furthermore, nongeometrical errors are caused by stick–slip motion, hysteresis, and nonlinear deformation due to impact and cutting forces during robot operations [20, 33]. The robot joints need to be integrated with a reducer with a high torsional stiffness and the ability for long-term operation in environments requiring high-speed performance [34, 35] to minimize nongeometrical impacts. Therefore, it is extremely important to choose a reducer with good structure, high torsional rigidity, high-speed operatability with a large payload ratio, and antivibration ability during machining [14]. Examples of reducers in the machining robot are compared in Table 3 [34, 35].

Table 3 Effects of the reducer on the performance of the machining robot [34, 35]
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3 Overview of Rigid Precision Reducers Used in the Actuator of the Machining Robot

Although several types of precision reducers are used in industrial robots [36], reducers with cycloidal disk and eccentric shaft are ideal for machining robots. Compared with a planetary reducer [37], the cycloid reducer can easily achieve a high reduction ratio without occupying a large working space. Owing to its circular tooth profile and multiple contact points, the cycloid reducer can work more efficiently and accurately than the planetary reducer. As shown in Table 3, the cycloid reducer has a much higher torque-to-weight ratio than the planetary reducer in a similar reduction ratio range, while still working with maximum efficiency under high-speed conditions. There is the other possible option for a joint reducer with a harmonic drive [35]. However, the harmonic drive has a continuously deformed and moving thin-wall structure causing it to have low torsional rigidity. This makes it suitable for applications with low load capacity and narrow space. [38]. The cycloid reducer is desirable for the machining robot under conditions requiring high accuracy and payload capacity, such as machining. Furthermore, the cycloid reducer is also known to exhibit high robustness and torsional stiffness with low required maintenance [34].

3.1 Operating Principle

Depending on the specific requirements of the applications, the cycloid reducer may have various structures, as shown in Fig. 2. The kinematic diagram of the cycloid reducer can be divided into five types: 2K-H, K-H-V, rotate vector (RV), China Bearing Reducer (CBR), and output-pin-wheel. The 2K-H type cycloid reducer consists of a planet carrier (H) and two central gears (K), as illustrated in Fig. 2a [39]. However, the 2K-H type cycloid reducer may have a high reduction ratio but low efficiency because it always need at least two gear pairs to transfer movement between input and output [40]. Thus, the K-H-V type cycloid reducer was invented to overcome the drawback of the 2K-H type by introducing an equal angular mechanism (V). The K-H-V type cycloid reducer is compact, lightweight, and highly efficient (Fig. 2b) [41]. The RV-type cycloid reducer using a combination of K-H and K-H-V cycloid reducers is proposed, as shown in Fig. 2c, to further increase the reduction ratio and enhance the flexibility of the output input [36]. Recently, a CBR-type cycloid reducer (Fig. 2d) was suggested for minimizing the volume; the outer diameter of the cycloid reducer would be similar in size to the harmonic drive [42]. The CBR-type cycloid reducer has disc connectors instead of the pin roller in the K-H-V-type cycloid reducer. Furthermore, an output-pin-wheel mechanism that works by switching functions between the output and housing using four cycloid disks, as shown in Fig. 2e, is proposed [43]. The kinematic diagram of the output-pin-wheel reducer is similar to that of the K-H type. Furthermore, the installed size can be increased. In general, the RV type cycloid reducer is the most widely used option in industrial robots nowadays.

Fig. 2
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Operating principle of various cycloid reducers

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3.2 Design Optimizations of the Cycloid Reducer

Design optimization is key to improving the performance of cycloid reducers. The performance of the cycloid reducer can be improved by using materials, lubrication methods, and design optimization. Various materials, from low-carbon steels to high-quality alloy steel, are used for cycloid reducers [44]. Alloy steels with Mn and Cr are widely used because of their hardenability, high bending strength, and fatigue strength [45]. Although Al is used in some parts of the harmonic drive owing to its lightweight, material choices for the cycloid reducer are limited because they have to guarantee structural stiffness of the reducer. Oil, grease, and mixed lubrication methods for cycloid reducers have advanced over the years [46, 47]. However, research related to the optimization of cycloid designs, since the first appearance of the cycloid reducer (over 60 years ago) (structure, tooth profile, etc.), is still ongoing from [48].

Design optimizations for cycloid reducers can be classified into three main groups: generating method of tooth profile, modification or correlation of the profile, and structural design. Several methods have been proposed to generate a cycloid profile for manufacturability. Tooth profile modifications or corrections are proposed to minimize the gaps between engaging elements. In particular, minimizing the initial gap (ideally 0) between engaged teeth pairs can significantly decrease transmission errors between output and input, which increases the accuracy of reducer. Lastly, most research related to reducer designs concentrates on the structural optimization of the cycloid reducer.

Methods for generating the cycloid tooth profile are divided into three main categories: circle enveloping [41, 49], transmitted coordinate systems [50,51,52], and instant-velocity center method [53, 54], as shown in Fig. 3. The circle-enveloping method generates a trace of a point of a circle rolling on the other fixed circle, which is called an epitrochoid curve, in coordinate system Fx (Ox, X, Y) [41]. The transmitted coordinate system method generates the epitrochoid curve by transforming points in the coordinate system with different frames of reference. This method normally uses three frames of reference Fg (Og, Xg, Yg), Fp (Op, Xp, Yp), Ff (Of, Xf, Yf) that are attached to the cycloid disk, cycloid pin (or cycloid wheel), and fixed-frame or housing [55,56,57]. The Fp of a cycloid pin coincides with Ff,, whereas Fp revolves around the origin of Ff, as illustrated in Fig. 3b. The instant-velocity center method utilizes three frames of reference similar to the transmitted coordinate system method and one more frame for the pitch point of the cycloid reducer (instant-velocity center). Thus, the generated epicycloid curve is determined according to the positions of the pitch point and contact point of the conjugating surfaces between the cycloid reducer and cycloid pins [53]. A comparison among the generating equations used in the three methods is presented in Table 4. The shape of the designed cycloid disk or the epicycloid curve depends on the radius of the pin roller, radius of the circle passing through the centers of the pin-rollers, eccentricity, number of pin-rollers, and number of teeth (or lobes of the profile) of the cycloid reducer.

Fig. 3
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Generating methods of cycloid tooth profile

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Table 4 Equations for cycloid tooth profile with different methods
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Modifications or corrections of the tooth profile should be performed to tolerate errors during both assembly and manufacturing processes [58, 59]. A small change in the theoretical tooth profile is made at the conjugated section of the tooth contact. Modifications or corrections of the tooth profile guarantee smooth engagement, increase the contact number, and provide good lubrication conditions [60, 61]. There are two types of tooth modification methods: single modified parameter and multi-modified parameter methods. The isometric, offset, and angular rotation modifications correspond to the single modified parameter method [54, 62]. Isometric and offset modifications are used to adjust the radius of the pin roller and the radius of the circle passing through the center of the pin rollers, respectively [62,63,64]. In contrast, the angular rotation modification changes the center position of the pin rollers along the circumferential direction [54, 62]. Isometric and offset modifications can be applied independently [63] or together [58], whereas the angular rotation modification can only be applied along with other methods [54]. Examples of single modified parameter and multimodified parameter methods are shown in Fig. 4 [64]. A comparison between various cases of a modified cycloid tooth profile with a theoretical profile is introduced by sole isometric modification (both positive and negative), and a combination of isometric and offset modifications. Furthermore, the multimodified parameter method of changing the tooth shape considering the pressure angle [59], increasing contact points [55], or under-cutting phenomenon [57] are presented. Finally, a tooth modification method is studied as a unified process of combining parameters such as machining tolerances and axial play in bearings [65].

Fig. 4
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Cases of profile modifications of the cycloid reducer [64] (open accessed). a 3D shape of the cycloid tooth profile, b Four modified cases of a cycloid tooth profile. *PM: positive roller radius modification; NM: negative roller position modification. NNM: negative roller position and negative roller radius modification. PPM: positive roller position and positive roller radius modification

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Various design problems of the cycloid reducer have been studied because the structure of a cycloid reducer has a significant effect on its performance [39, 52, 59]. As mentioned in the previous section, five types of cycloid reducers are introduced to improve their performance, including size, payload, strength, and stiffness [52, 66]. Furthermore, the output mechanism of a cycloid reducer has a significant impact on the torsional stiffness and vibration [67,68,69]. A cycloid reducer structure without pin rollers was proposed to decrease the stress fluctuation associated with conventional designs [70]. This research also recognized that the presence of more than two tooth differences reduces stress fluctuations and velocity ripple, in addition to improving the stress distributions of the cycloid reducer. In contrast, reducing the difference in tooth number between two pin-rollers of the 2K-H type cycloid reducer can improve the self-locking performance of the mechanism but degrade the backlash angle of the reducer [39].

All aspects of the tooth profile and the cycloid reducer designs are summarized in Fig. 5.

Fig. 5
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Design optimizations of the cycloid reducer

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4 Performance Analysis of the Cycloid Reducer

Internal and external factors affecting the performance of the cycloid reducer, as shown in Fig. 6. The tooth geometry and bearing characteristics are the most significant internal factors affecting the load capacity, rigidity, bending stress, and torque ripple of the transmission device [71]. On the other hand, machining errors or tolerances of the components of a cycloid reducer increase backlash, lost motion, and transmission errors, in addition to causing vibration and noise in the system [58, 72]. Nevertheless, both the payload and speed are external factors that significantly influence the efficiency of the reducer, whereas the assembling misalignment between the reducer and input or output parts affect the vibration/noise and shock resistance of the system [73, 74].

Fig. 6
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Factors affecting the performance of a cycloid reducer

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A mathematical model of the contact point and force distribution of a cycloid reducer is required, considering that the contact force distribution is a fundamental in investigating tooth stress and dynamic transmission performance analysis. Dynamic equations for the contact force distribution in the meshing area of a 2K-H cycloid reducer are derived in [39]. A detailed analysis of the dynamic model of the eccentric shaft bearing is performed to evaluate the engagement of a cycloid reducer [75, 76]. Recently, stress analysis of a cycloid reducer was performed by combining the kinematics and dynamics of rigid bodies and nonlinear stiffness based on contact dynamics [77].

As mentioned in the previous section, the structures of the reducer as well as the tooth profile and its modification strongly affect the force distribution, hysteresis curve, transmission errors, and efficiency [67]. The contact number and force distribution of a cycloid reducer are numerically studied considering two tooth modification methods, i.e., isometric and offset methods, and their effects on the torque performance of the cycloid reducer are analyzed [64]. Tooth profile modifications based on the contact angle (straight line, catenary, and cycloid functions) reduce the backlash and lost motion of the cycloid reducer significantly compared to conventional tooth modifications, as shown in Fig. 7 [59]. In addition, high stress concentrated on the contact points of a cycloid reducer such as pin-rollers could be relieved by performing FE analysis and design modifications [78, 79]. Longitudinal tooth profile modifications are also effective in smoothing the contact distribution [64, 80] as well as performance— efficiency [66], transmission error [60, 76], and torsional rigidity [81]. As an example, the transmission error of an RV-type reducer can be reduced by 24%, with proper tooth modification, as shown in Fig. 8 [52]. The nonpin A cycloid reducer without pinwheels [51] might exhibit higher efficiency under certain conditions than those with pinwheels [82].

Fig. 7
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Influence of modified tooth profile methods on the backlash and lost motion of a cycloid reducer [59] (open access)

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Fig. 8
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Initial clearances, normal contact deformations, and transmission errors of a proposed tooth profile [52] (open access)

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Bearings used in a cycloid reducer significantly influence the performance of the cycloid reducer, which can be studied using numerical or FEM analysis [83]. In particular, the RV-type reducer has many bearings, making it suitable for investigating the effects of bearings on the dynamic performance of reducer [76, 84, 85]. The stiffness and geometric deflects of bearings may affect the contact force distribution and finally lead to an improvement in the vibration sensitivity and reliability of the cycloid reducer [75, 85]. Moreover, the clearance of the support bearings might affect the transmission errors of a cycloid reducer [84]. Lastly, a cycloid reducer with needle roller bearings has better efficiency than that with sleeve bearings [86].

The machining quality of the tooth profile is also a significant contributor to the performance of cycloid reducers [87, 88]. Specifically, the torsional stiffness of a cycloid gear is strongly related to the roughness of the tooth surface [87]. In addition, the clearances of the cycloid reducer due to machining errors have an impact on the hysteresis curve of the reducer, such as backlash and lost motion [88]. Finally, the manufacturing tolerance of eccentricity might also affect the force distribution and power losses of a cycloid reducer [74].

The efficiency and life cycle of the cycloid reducer are governed by friction and lubricants. The friction forces of both sliding and rolling motions cause losses in the cycloid reducer [69]. Experiments were conducted to investigate the correlation between the friction/lubricant and power losses/efficiency of the cycloid reducer [86]. As the speed increases, the friction coefficient [89] and the contact ratio decrease [61]. The contact force distribution of a cycloid reducer also influences the average film thickness and efficiency of the reducer [61]. Oil lubrication enables a large compound cycloid reducer to dissipate heat effectively from friction loss [90]. Furthermore, oil filling can be used in diagnosing a cycloid reducer, and abrasive friction particles should be carefully checked to extend the life cycle of the cycloid reducer [91].

The performances of the cycloid reducers are investigated experimentally, as shown in Figs. 9 and 10. The experimental setup is divided into four principal subsystems: assembly, instrumentation, supervision, and interface, as shown in Fig. 9. All components connected in the transmission system are denoted by "assembly.” “Instrumentation” includes high precision sensors, such as an angle encoder, torque meter, and speed meter. Usually, the control system drives the input angle of the motor through a motor driver and applies a torque load via a brake or servomotor. Finally, the "interface" helps to collect and show the data. All data from "instrumentation" are collected and displayed on a computer.

Fig. 9
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Principal subsystems of an experimental setup of a cycloid reducer

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Fig. 10
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Schematic of an experimental system of a cycloid reducer

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The impacts of operating payload, speed, and misalignment errors on the performance of the cycloid reducer can be experimentally studied. Integrated with internal effects, an experimental system with a precision reducer might operate with slightly lower performance, including having higher transmission error [71, 73], lower torsional stiffness [67, 92], and more vibrations [92, 93]. Even though the efficiency could be improved under certain conditions, such as high input torque and low speed, many losses would still be present in the entire experimental system [86, 89]. Thus, vibration suppression and suitable lubrication approaches would have to be carefully considered to improve the experimental conditions of the cycloid reducer [73, 91].

5 Machining Process and Fault Detections of the Cycloid Reducer

Grinding is the principal method for producing an accurate epicycloid profile of a cycloid reducer [94]. Generally, the milling process with a 5-axis CNC machine can create the tooth profile of a cycloid gear [95], but the grinding process can provide better roughness for the tooth surface of a cycloid gear [87]. With the recent improvement in precision measurement technology and gear grinding devices [96], all technical aspects of forming a complex surface, such as an epicycloid, can be handled using the grinding process. A grinding system for cycloid gear quantitatively corrects the error of the tooth profile of a cycloid reducer, with an eccentric shaft and pin rollers. The only difference is that one of the pin rollers is replaced with the grinding wheel, as shown in Fig. 11 [94].

Fig. 11
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Grinding system and process for machining the cycloid gear [93]. (open access)

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In addition, selective parts of cycloid reducers are assembled using a genetic algorithm for better performance [97]. A fault detection method is applied to discard poor quality products of cycloid reducers [98], which are usually based on vibration signals [99] or acoustic emission [100, 101].

6 Other Applications of Rigid Precision Reducer

Owing to their high-performance characteristics such as accuracy, reliability, and rigidity, cycloid reducers are widely being used in various applications, as illustrated in Fig. 12. First, a cycloid reducer is designed with an extremely compact size and unified with a servomotor in a light-weight actuator, which is suitable for mobile robots [102,103,104]. Moreover, medical equipment and surgical robots use a cycloid reducer as a component in an automatic tool changer or actuator [105]. In the automotive industry, a cycloid reducer is used in E-CVVT [106, 107] or the new upgraded system E-CVVD [108] as an actuator. In addition, a cycloid reducer is used as an actuator in vehilce radar systems [109].

Fig. 12
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Other applications of the cycloid reducer

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7 Conclusion

Although smart manufacturing is a strong industrial driver for reshaping the current competitive landscape and establishing new market leaders, machining manufacturing plays an irreplaceable and dominant role in manufacturing. Machining robots are leading the change in the existing manufacturing system, and the precision reducer is an important component governing the accuracy of the machining robot. The cycloid reducer is the best candidate among precision reducers when considering both the structural compliance and kinematic accuracy of the machining robots. Many types of cycloid reducers have been developed, and numerous design approaches to improve the performance of cycloid reducers have been proposed. Performance evaluations for the cycloid reducer are necessary for validating the proposed designs. In addition, fault detection and diagnosis issues are gaining interest from researchers. Currently, cycloid reducers are finding industrial applications such as in mobility, automotive, and precision industrial robots. Thus, the application of cycloid reducers will continue to expand.