1. Introduction

2. Methodology

3. Applications and Architectures

3.1. Machining

Figure 3 shows that machining is the most popular application of parallel-serial manipulators. This is because parallel-serial manipulators combine the benefits of parallel and serial architectures, providing high rigidity, motion accuracy, and workspace, which are critical for machining operations. These operations are not limited to milling or drilling but include grinding, polishing, welding, and sheet forming.

The literature review reveals that existing parallel-serial machining manipulators differ mainly in their underlying parallel mechanisms. Therefore, we found it convenient to classify the manipulators according to this mechanism. The rest of the subsection will illustrate this classification and cover various architectures of hybrid machining robots.

3.1.1. Manipulators Based on the Tricept Parallel Mechanism

Manipulators in this family are based on a 3-DOF parallel mechanism called Tricept and patented by Neumann [31]. This mechanism has one UP branch, which defines the motion type of the output link, and three UPS branches, which include actuators. Based on this scheme, scholars have proposed different parallel-serial manipulators considered next.

Tetrabot (tetrahedral robot) [32] was probably the first ever parallel-serial manipulator, which was used for assembly operations. In this robot, the output link of the Tricept parallel mechanism is augmented with an RRR serial spherical wrist (Figure 4a). This 6-DOF kinematics has become suitable for other applications as well. For example, Choi and Lee [33] considered using this parallel-serial manipulator for propeller grinding and developed its physical prototype. In the prototype, the serial wrist was designed as a geared mechanism. The authors analyzed the kinematics, dynamics, and position/velocity control of this manipulator in their paper [34]. Zhao et al. [35] designed another prototype of such a parallel-serial manipulator and applied it to polishing operations. In their later works, the authors focused on kinematic calibration [36], stiffness [37] and repeatability [38] analysis, and different control strategies [39,40] of this robot.

While 6-DOF manipulators can reach any desired end-effector posture, most machining operations only need five DOFs to position and align the tool. In this regard, most Tricept-based parallel-serial robots are equipped with a 2-DOF RR serial wrist (Figure 4b). The obtained (1-UP/3-UPS)RR architecture is the one that is actually called Tricept in most cases. Parallel-serial manipulators with this architecture have been the subject of numerous articles and successfully applied in practice [41]. For example, among the pioneering studies are the works of Siciliano [42,43], who analyzed the inverse and direct kinematics of this robot but focused mainly on the 3-DOF parallel part. Milutinović et al. [44] continued these studies and considered the kinematics of the serial wrist, while Eastwood and Webb [45] used these kinematic models and discussed how thermal deformations affect the positioning accuracy of the robot. Besides conventional milling and drilling operations, the Tricept parallel-serial manipulator has been used for incremental sheet forming [46,47], friction stir welding [48,49], and optical polishing [50,51]. Most recent applications include processing large optical mirrors [52,53,54].

The actuated branches of the Tricept manipulator have a UPS architecture where the universal joint is located at the base. An SPU branch with the spherical joint placed at the base is a natural kinematic equivalent of this architecture, and other scholars have also considered Tricept manipulators with these branches (Figure 4c). Thus, Kim et al. [55] developed such a (1-UP/3-SPU)RR parallel-serial manipulator, analyzed its kinematics [56] and dynamics [57,58], and performed a kinematic calibration of the physical prototype [55]. Another kinematically equivalent design was proposed by Tönshoff et al. [59], who developed a Georg V manipulator with three PUS branches, featuring actuated prismatic joints at the base (Figure 4d).

Inspired by the successful design of Tricept, scholars proposed different Tricept-based architectures of parallel-serial manipulators. For example, Li et al. [60] considered a 4-DOF (1-RP/2-RPS)RR robot called Bicept (Figure 4e). This robot includes a 2-DOF planar Tricept-like parallel mechanism where spherical joints are used to compensate for misalignment and can be replaced with revolute joints. The robot stiffness and performance were examined in papers [61] and [62], but all the analysis was done for the planar parallel mechanism.

Figure 4. Parallel-serial machining manipulators of the Tricept family: (a) (1-UP/3-UPS)RRR (Tetrabot) [32]; (b) (1-UP/3-UPS)RR (Tricept) [42]; (c) (1-UP/3-SPU)RR [55]; (d) (1-UP/3-PUS)RR (Georg V) [59]; (e) (1-RP/2-RPS)RR (Bicept) [60]; (f) (1-UP/2-UPS)RR (TriVariant) [63]; (g) (1-U/2-UPS)PRR (TriVariant B) [64]; (h) (1-UP/3-UPS)PRR (Tricept IV) [65]; (i) (R(1-RP/2-RPS)/1-UPS)RR (TriMule) [66]; (j) (R(1-RP/1-RPS)/2-UPS)RR (Trifree) [67]; (k) (R(2-RPR)U/1-UP)RR [68]; (l) (R(1-RP/1-RPR)/1-UPS)RR [69]; (m) (R(4-RPR)/(2-RPR)R)RR [70]; (n) PP(1-UP/3-UPS) [71]; (o) PP(1-PU/2-UPS) [72]; (p) (1-PU/2-PSS)PP [73].

Figure 4. Parallel-serial machining manipulators of the Tricept family: (a) (1-UP/3-UPS)RRR (Tetrabot) [32]; (b) (1-UP/3-UPS)RR (Tricept) [42]; (c) (1-UP/3-SPU)RR [55]; (d) (1-UP/3-PUS)RR (Georg V) [59]; (e) (1-RP/2-RPS)RR (Bicept) [60]; (f) (1-UP/2-UPS)RR (TriVariant) [63]; (g) (1-U/2-UPS)PRR (TriVariant B) [64]; (h) (1-UP/3-UPS)PRR (Tricept IV) [65]; (i) (R(1-RP/2-RPS)/1-UPS)RR (TriMule) [66]; (j) (R(1-RP/1-RPS)/2-UPS)RR (Trifree) [67]; (k) (R(2-RPR)U/1-UP)RR [68]; (l) (R(1-RP/1-RPR)/1-UPS)RR [69]; (m) (R(4-RPR)/(2-RPR)R)RR [70]; (n) PP(1-UP/3-UPS) [71]; (o) PP(1-PU/2-UPS) [72]; (p) (1-PU/2-PSS)PP [73].

Huang et al. [63] introduced a TriVariant manipulator (Figure 4f), where one UPS was removed and the drive was displaced to the UP branch, which became the UP actuated branch. This manipulator has been the subject of many studies, which considered its kinematics [63,74,75], dynamics [76], stiffness analysis [77], dimensional synthesis [78], and calibration [79]. Most of these studies, however, focused on the 3-DOF parallel part. The TriVariant manipulator was later modified into TriVariant B [64], where the actuated prismatic joint was moved to the serial chain, so the robot architecture became (1-U/2-UPS)PRR (Figure 4g). The authors analyzed its kinematics [64], dynamics [80], and stiffness [81], with a major focus on the 2-DOF parallel mechanism.

Based on the Tricept and TriVariant B designs, Sun et al. [65] proposed a novel parallel-serial manipulator, Tricept IV, with the (1-UP/3-UPS)PRR architecture (Figure 4h). In this manipulator, the prismatic joints in the UP branch and the PRR serial chain are coaxial, which results in kinematic redundancy and increases the manipulator workspace. The authors evaluated the stiffness of this robot [65,82], performed its dimensional synthesis [83], and also considered the robot application for friction stir welding [84].

In the Tricept-based parallel-serial manipulators discussed so far, the parallel mechanism had three or four branches attached to the base. Scholars soon discovered how to simplify and lighten the design by combining the base joints of these branches [66]. This idea led to the development of the TriMule robot [66,85]—one of the most studied parallel-serial manipulators at the moment. In this robot, the universal joints of the UP branch and two UPS branches share a yoke that rotates relative to the base (Figure 4i). We can notate the TriMule architecture as (R(1-RP/2-RPS)/1-UPS)RR and see it has only two joints placed on the base, simplifying the robot design. The TriMule manipulator has become the subject of many papers devoted to its kinematics [86,87], dynamics and gravity compensation [88,89,90,91,92], stiffness [93,94,95,96], performance evaluation [97,98], optimal design [99], path planning [100,101,102,103], feed rate scheduling [104,105,106], calibration [107,108,109,110,111,112,113,114,115], and control [116,117,118,119,120]. Diverse applications of the TriMule robot include helical milling [121], collaborative mirror milling of large thin-walled parts [13,122,123,124,125], grinding [126], friction stir welding [127,128,129,130,131,132], and trimming unidirectional carbon fiber-reinforced polymers [133]. Apart from these, the TriMule robot was mounted on a mobile platform and applied for large-scale machining of aerospace components [134,135]. There also exists a 6-DOF TriMule design with a 3-DOF RRR spherical wrist, as in Tetrabot [136].

The TriMule success inspired scholars to develop other similar parallel-serial manipulators. For example, Wang et al. [67] proposed a Trifree robot with an (R(1-RP/1-RPS)/2-UPS)RR architecture (Figure 4j), where the universal joints of two branches had a common yoke. The authors analyzed the kinematics and dynamics of this robot in their works [137] and [138]. Li et al. [68] presented an (R(2-RPR)U/1-UP)RR manipulator (Figure 4k), whose parallel mechanism had only three branches, and performed dimensional synthesis of this mechanism. Another design with three branches was introduced by Dong et al. [69], who used an asymmetrical (R(1-RP/1-RPR)/1-UPS)RR architecture (Figure 4l). Finally, Liu et al. [70] considered a super redundantly actuated (R(4-RPR)/(2-RPR)R)RR manipulator, whose parallel mechanism had three DOFs and six drives (Figure 4m). To our knowledge, all these novel manipulators exist only as computer models; no physical prototypes have been created.

All previous parallel-serial manipulators were equipped with a 2- or 3-DOF spherical wrist. There also exist Tricept-based architectures without this wrist but with a PP serial kinematic chain. Thus, Luo et al. [71] proposed a PP(1-UP/3-UPS) robot with a parallel mechanism placed on the PP moving frame (Figure 4n). A similar design with a 1-PU/2-UPS parallel mechanism was introduced by Shan et al. [72], who placed this mechanism on the XY moving table and used it as a spindle posture alignment device (Figure 4o). One more design was devised in paper [73], where the PP serial kinematic chain was placed on the platform of the 1-PU/2-PSS parallel mechanism (Figure 4p). This manipulator is intended to process machine components with complex and/or longitudinal shapes, and studies [139] and [140] analyzed its kinematics, including workspace and singularities. All these listed manipulators, however, are only available as computer models.

3.1.2. Manipulators Based on the Sprint Z3 Parallel Mechanism

The parallel-serial manipulators discussed in this subsection rely on the Sprint Z3 parallel machine tool patented by Wahl [141].1 Unlike Tricept, this parallel mechanism does not have a passive branch but includes three symmetrically arranged PRS branches. Each branch imposes one constraint, leaving the output link with two rotational and one translational DOFs. Numerous papers have studied this parallel mechanism [10], but we will focus on parallel-serial manipulators based on its kinematics.

The first example is the Ecospeed machine center [143], which includes this 3-PRS parallel mechanism mounted on a 2-DOF PP serial chain (Figure 5a). San et al. analyzed the kinematics and error sources of this parallel-serial manipulator in their recent work [152]. Other scholars also considered a 4-DOF P(3-PRS) architecture, which was used with a 1-DOF moving table. Multiple studies examined the error sensitivity [153,154], stiffness analysis [155], calibration [156,157,158,159], and control [160,161,162] of this robot. Huang et al. [23] developed a similar manipulator where the revolute joints were replaced with parallelogram joints (Figure 5b). The authors considered the dynamics [163], calibration [164,165], and control [166] of the manipulator, focusing on its 3-DOF parallel part. The actuated parallelogram joints were used in an RRRP(3-PaRS) manipulator [144] (Figure 5c), based on a 4-DOF SCARA-type serial chain and a 3-DOF CaPaMan (Cassino Parallel Manipulator). The authors made a prototype of this manipulator for wood drilling and considered its position and force control. A SCARA-type serial chain was also used in a (3-PSP)RRRP manipulator [145], attached to the moving platform of the parallel mechanism (Figure 5d). This 7-DOF manipulator was designed for welding operations inside a steam generator, and the authors analyzed the robot workspace and control in the cited paper.

The architectures mentioned above included actuated prismatic or parallelogram joints near the base of the parallel mechanisms. There are also manipulators where these joints are placed in the middle of the branches. For example, Wang et al. [146] developed a 6-DOF PPP(3-RPS) robot (Figure 5e) for marine propeller processing and addressed its kinematic calibration in paper [167]. A similar parallel mechanism was used in a P(3-RPS)R manipulator (Figure 5f) designed for blade machining and polishing [147]. The authors applied this manipulator with a 1-DOF moving platform and performed its calibration in work [168]. Li et al. [148] “inverted” the branches of the parallel mechanism and introduced a (3-SPR)RR architecture (Figure 5g). The authors analyzed the performance [169] and stiffness [170,171] of this manipulator and discussed its calibration [172], with the main focus on the parallel part. Li et al. [149] proposed a robot with one RPS and two SPR branches (Figure 5h) and examined its kinematics and performance. This manipulator was designed for friction stir welding and was supposed to operate with a 1-DOF moving table, but as far as we know, there is no physical prototype of this robot.

There also exist several architectures where a parallel mechanism has a universal joint in its branches. For example, Chong et al. [24] introduced a PaPa(3-RCU) manipulator (Figure 5i) aimed at polishing wind turbine blades. Here, C means passive revolute and actuated prismatic joints with collinear axes. The 2-DOF PaPa serial chain had a complex actuation scheme, omitted in the figure, and was placed on a mobile platform to increase the robot workspace. The authors performed the elasto-geometrical calibration of this robot [173] and considered its control strategies [174]. Another polishing robot was designed by Xu et al. [150] and included a 3-DOF 3-UPR parallel mechanism attached to a 6-DOF serial manipulator (Figure 5j). Unlike the previous architectures discussed in this subsection, the parallel mechanism is overconstrained. The authors studied the robot dynamics and control and performed its dimensional synthesis in the cited paper, focusing on the parallel part. Finally, we would like to mention a PP(1-PUS/3-RHUR) manipulator (Figure 5k) proposed by Tian et al. [151]. The parallel mechanism of the manipulator includes a PUS branch to increase the large-stroke stiffness of this mechanism. The authors analyzed kinematics and performed a multi-objective design optimization of this robot, which currently exists only as a computer model.

3.1.3. Manipulators Based on the Exechon Parallel Mechanism

Manipulators discussed in the two previous subsections were based on 3-DOF non-overconstrained parallel mechanisms. Scholars also considered the use of overconstrained parallel mechanisms in parallel-serial manipulators. One of the most notable manipulators in this family is the 5-DOF Exechon robot proposed by Neumann [175]. It includes a 3-DOF overconstrained parallel mechanism with one SPR central branch and two 2-UPR lateral branches, where the base axes of the universal joints are collinear (Figure 6a). The output link of the parallel mechanism is equipped with an RR spherical wrist. This manipulator has been successfully applied in industry [176], including optical [177] and large-scale [178,179,180] machining. Numerous articles performed its mobility [181], kinematic [182,183,184], and stiffness [185,186,187,188] analyses, as well as calibration [189]. Some scholars studied Exechon manipulators with offsets in the base joints [190,191] and both the base and the wrist joints [192,193,194,195]. Sagar et al. [196] also considered a 7-DOF kinematically redundant design with a 4-DOF serial chain developed for placing fixture heads along sheet metal (Figure 6b).

Inspired by the Exechon success, scholars proposed different modifications of its design. For example, Li et al. [197] inverted the central branch of the parallel mechanism and considered the (1-RPS/2-UPR)RR architecture (Figure 6c). In their study, the authors performed a multi-objective dimensional synthesis of this robot. Tengfei et al. [198] inverted the lateral chains and developed a (1-RPS/2-RPU)RR parallel-serial manipulator called Exe-Variant (Figure 6d). Paper [207] evaluated its workspace and performance. The authors also considered a variation of this design where this parallel mechanism was placed on a PR serial chain [199] (Figure 6e), whose revolute joint represented a carriage moving along a circular rail. This architecture provides a large workspace essential for machining aeronautic components, as the authors discussed in their paper. Jin et al. [200] proposed a PP(1-SPR/2-RPU) parallel-serial robot for similar applications (Figure 6f). However, as we know, all the manipulators discussed in this paragraph exist only as computer models.

The aforementioned manipulators were developed by inverting the central and/or lateral branches of the 3-DOF parallel mechanism. Other scholars also modified the structure of these branches. For example, Xu et al. [201] introduced a 4-DOF manipulator with the 1-UPR central branch (Figure 6g). This manipulator, operating with a 1-DOF moving table, has been the subject of multiple studies that have focused on its kinematics [208], dynamics [209], stiffness [210], optimal design [211,212], and calibration [213]. Zhang et al. [202] changed the structure of all branches and proposed a PP(1-PRPS/2-PRU) manipulator with redundant actuation (Figure 6h). The authors analyzed the mobility and workspace of this robot, focusing on its parallel part. Another original design with one SP and two UPU branches and an RR spherical wrist was introduced in work [203] (Figure 6i). This manipulator has also become the subject of many studies devoted to its kinematics [214,215], dynamics [216,217,218], stiffness [219,220,221], and calibration [222]. Finally, Xu et al. [204] developed an RP(1-RRS/2-RRU) inner-cavity machining robot without prismatic joints in the parallel mechanism (Figure 6j). The authors studied the robot kinematics and dynamics, performed its dimensional synthesis, and designed a 3D-printed prototype.

There are also Exechon-inspired parallel-serial manipulators whose parallel mechanism has four branches. Thus, Yue et al. [205] proposed a (1-SPR/1-SPR/2-UPU)RR architecture with one passive branch (Figure 6k). In their work, the authors analyzed the mobility and kinematics of this robot and performed its dimensional optimization. Zhang et al. [206] presented a PP(2-RPU/2-SPR) redundantly actuated manipulator (Figure 6l) and considered its kinematics [206], dynamics [223], stiffness analysis [224], and optimal design [225]. The authors focused mainly on the 3-DOF parallel mechanism and developed a physical prototype only for this mechanism.

3.1.4. Manipulators Based on Planar Parallel Mechanisms

This subsection will cover parallel-serial machining manipulators based on parallel mechanisms whose end-effector performs planar motion. We can classify these manipulators into two groups, as discussed next.

The first group includes manipulators with 2-DOF parallel mechanisms. For example, Li et al. [226] proposed a 3-DOF (1-PR/1-PRR)P architecture (Figure 7a). The authors analyzed the kinematics of this hybrid robot and developed its prototype. Ma et al. [227] introduced a 5-DOF P(1-RP/1-RPR)RR manipulator with an RR spherical wrist (Figure 7b). Unlike the previous design, the prismatic actuators of the parallel mechanism were connected to its base by revolute joints. A similar architecture was considered by Wang et al. [228] who used a 1-RR/1-RRR parallel mechanism as a parallel module (Figure 7c). The authors applied this robot for machining large casting parts and discussed simulations and experiments in paper [229]. Uchiyama et al. [230] designed a (1-PR/1-PRP)PRR manipulator for robotized deburring operations (Figure 7d). The authors studied the kinematics of this robot and proposed a continuous path control algorithm, which was successfully applied in practice. Another 5-DOF manipulator with an identical PRR serial chain was developed by Guo et al. [231]. Unlike the architectures above, the 2-DOF planar parallel mechanism had one PR passive branch and two PRP branches with prismatic actuators at the base (Figure 7e). In their later works, the authors analyzed workspace [232], dynamics [233,234], and control [235] of this robot.

The second group includes manipulators with 3-DOF parallel mechanisms, and there are just a couple of architectures within this group. The first is a (3-RRR)PRR manipulator developed by Yang et al. [236] for deburring operations (Figure 7f). The authors created a robot prototype with a modular design, and its kinematic analysis can be found in studies [237] and [17]. Finally, paper [73] introduced a (2-RPR/2-RRR)PR redundantly actuated manipulator for processing elongated objects (Figure 7g). At the moment, this manipulator exists only as a computer model, and its kinematics has been analyzed recently in works [238,239].

3.1.5. Manipulators Based on the Delta Parallel Mechanism

The Delta mechanism, proposed by Clavel [240], has become one of the most successful parallel architectures. The output link of this mechanism has three translational DOFs provided by parallelogram joints in its branches. However, there are just a few examples of Delta-based parallel-serial manipulators applied for machining, possibly because of their lower rigidity compared to other architectures discussed in the previous subsections.

The first example is the JDYP51 polishing machine tool [241] based on the Delta mechanism with prismatic actuators (Figure 8a). The output link of the parallel mechanism is equipped with an RR spherical wrist. Paper [245] analyzed manipulator stiffness, and the authors of [246] optimized the polishing process performed with this robot. Xu et al. [242] introduced another polishing manipulator based on the Delta mechanism. Unlike the previous design, the branches of this mechanism use spatial parallelogram joints with spherical joints (Figure 8b). A 1-DOF serial chain connects to the moving platform by a revolute joint, actuated by an auxiliary RUPU branch, which is omitted in the figure for clarity. This 4-DOF parallel-serial manipulator moves the processed object, while the polishing tool is placed on an independent 2-DOF serial mechanism. In the later works, the authors considered path planning [247], dynamics [248,249], stiffness [250], optimal design [251], calibration [252], and control [253] of this robot, focusing on the parallel part.

Other examples of Delta-based manipulators include kinematically redundant architectures, which, to our knowledge, exist only as computer models. Thus, Mohammadipanah and Zohoor [243] proposed an 8-DOF hybrid robot with an RRRRR serial chain (Figure 8c). The authors considered its application for arc welding and analyzed the kinematics and dynamics of this manipulator. Nguyen et al. [244] studied a 9-DOF macro-mini milling robot where the Delta mechanism was attached to the end-effector of the 6-DOF Kawasaki RS030N industrial manipulator (Figure 8d). The main focus of the authors’ work was on the compliance analysis and error compensation of this robot.

3.1.6. Manipulators Based on the Gough–Stewart Platform

The 6-DOF Gough [254] or Gough–Stewart [255] platform is another successful parallel mechanism used in numerous applications [256]. This mechanism has six UPS branches that provide its output link with high stiffness and positioning accuracy. However, we have found just a few examples of parallel-serial machining manipulators based on the Gough–Stewart platform. The reason is that these manipulators will have kinematically redundant architectures with more than six DOFs, which are rarely needed for machining purposes.

On the other hand, such redundancy can increase the workspace of the parallel mechanism. Thus, Wu et al. [257] developed a 10-DOF parallel-serial manipulator called IWR (Intersector Welding Robot), where the Gough–Stewart platform was mounted on a PPRR serial chain (Figure 9a). This robot was designed for assembly operations in the vacuum vessel of ITER (International Thermonuclear Experimental Reactor). There are multiple studies devoted to stiffness analysis [258,259,260], calibration [261,262,263,264,265], and control [266,267,268,269] of this robot. In works [270] and [271], the authors also considered a 7-DOF prototype of this manipulator with a 1-DOF serial chain (Figure 9b). Finally, we can mention study [272], whose authors installed the Gough–Stewart platform on the end-effector of a 6-DOF UR5e robotic arm (Figure 9c). This parallel-serial manipulator was applied to position a touch probe.

3.1.7. Other Manipulators

This subsection will cover parallel-serial manipulators, which we cannot put in any of the previous groups. It is interesting that there are just a few manipulators in this family, and we have found only two architectures with working prototypes used in practice.

The first example is the 6-DOF RNT (Robot of a New Type) developed by Mianowski et al. [273] for milling and polishing large objects. This robot features a 2-DOF 1-RR/2-UPS parallel mechanism placed on the rotating base, and the output link of this mechanism is equipped with an RRR spherical wrist (Figure 10a). The authors considered the design, control, and applications of RNT in their later studies [281] and [282]. The second example is the 7-DOF CraftsRobot [274], which was also applied for processing large-scale objects. The robot includes a 5-DOF 1-UCR/4-UCU parallel mechanism attached to the PaPa serial chain with the same architecture as in the previously discussed PaPa(3-RCU) manipulator [24] (Figure 10b). Similar to that work, the parallel-serial manipulator was installed on the moving platform, which increased its workspace. In recent works, scholars have considered the stiffness [283], optimal design [284], and error compensation [285] of this hybrid robot.

Other manipulators considered below exist only as computer models. There are several architectures based on 4-DOF parallel mechanisms. For example, Lu et al. [275] introduced a PP(1-PRU/3-PUS) manipulator and analyzed the workspace and dynamics of its parallel part (Figure 10c). Another design was considered by Tian et al. [276], where one PUS branch was replaced with the second PRU branch (Figure 10d). The authors performed the mobility analysis of this robot and found that it had no singular configurations. Li et al. [277] studied a similar P(2-RPU/2-UPS) architecture where prismatic actuators of the parallel mechanism were displaced to the middle of its branches (Figure 10e). In their paper, the authors considered the kinematics and dynamics of this parallel-serial manipulator. Finally, Tian et al. [278] modified their previous design and proposed a robot where all the universal joints of the parallel mechanism were placed on the base (Figure 10f). The authors studied the robot kinematics and performed its dimensional synthesis.

To conclude this subsection, we would like to mention two manipulators based on 3-DOF parallel mechanisms. The first one is a 5-DOF manipulator with a 3-PUU translational parallel mechanism considered by Wang et al. [279] (Figure 10g). The manipulator was intended for polishing, and the authors optimized the polishing process in their study. The second example is a (3-UPU)RRR hybrid machining robot introduced by Dou et al. [280] (Figure 10h). In their work, the authors performed a comprehensive stiffness analysis of this manipulator.

3.2. Medicine

Medicine is the second most popular sphere where parallel-serial manipulators find their use (Figure 3). Unlike the previous subsection, where we classified machining manipulators by the underlying parallel mechanism, we found it more convenient to classify medicine hybrid robots by application. The rest of this subsection will consider these applications and corresponding parallel-serial manipulators in more detail.

3.2.1. Manipulators for Minimally Invasive Surgery

Minimally invasive surgery implies performing operations with a single incision point of the instrument. Scholars have developed various parallel-serial manipulators to position the instrument in such a way. One of the most famous and well-studied robots is PARAMIS, proposed by Plitea et al. [286]. This 5-DOF manipulator included a 2-DOF planar parallel mechanism placed on the revolute base and equipped with an RR serial chain (Figure 11a). There are many papers devoted to kinematics [287,288,289], dynamics [290], control [291], and simulations [292,293] of this robot, while study [294] considered a modified design of the RR serial chain. Based on PARAMIS, Pisla et al. introduced PARASURG 5M-1 [295] and 5M-2 [296] manipulators with a 1-PR/1-PRR parallel mechanism (Figure 11b and Figure 11c). The difference between the 5M-1 and 5M-2 architectures is in the joint arrangement of the RR serial chain. The authors analyzed the kinematics [297] and dynamics [298,299] of both architectures, while Stoica et al. [300,301,302] and Szilaghyi et al. [303,304] considered the actuation of the RR chain using auxiliary kinematic chains. The 5M-2 design has become the basis for another robot, PARASURG 9M [305], where the serial chain was equipped with a 4-DOF instrument. It included a 3-DOF miniature spherical parallel mechanism and a prismatic joint—Figure 11d shows a simplified representation of the PARASURG 9M manipulator. In later works, scholars analyzed the mobility [306], kinematics [307,308], and control architecture [309,310] of this robot. A similar 1-PR/1-PRR planar parallel mechanism was also used in two 5-DOF parallel-serial manipulators, proposed by Peng et al. [311] and Li et al. [312] for spine surgery (Figure 11e and Figure 11f). The architectures of the manipulators differ only by the joint order in the 3-DOF serial chain. In their studies, the authors focused on the kinematics, optimal design, and control of these two robots.

The design of several parallel-serial manipulators provides its end-effector with a fixed incision point called a remote center of motion (RCM). One way to obtain an RCM is to use a spherical mechanism. Thus, Degirmenci et al. [313] introduced a 6-DOF PPP(1-RR/1-RRR)R manipulator for microsurgery, which included a 2-DOF parallel spherical mechanism (Figure 11g). In their study, the authors analyzed the robot performance and developed its physical prototype. Tucan et al. [314] presented a similar 5-DOF manipulator where the spherical mechanism had a circular rail (kinematically equivalent to a revolute joint, as shown in Figure 11h). The authors considered the kinematic modeling of this robot. Circular rails were also used for intermediate revolute joints in a 4-DOF (1-RR/1-RRR)PR manipulator proposed by Cao et al. [315] (Figure 11i). In their paper, the authors performed a dimensional synthesis of this robot but focused mainly on the 2-DOF parallel part. Li et al. [316] introduced another 4-DOF robot with an original 1-RRPR/1-RRRR 2-DOF parallel mechanism and a similar PR serial chain (Figure 11j). The authors’ study was devoted to the kinematic analysis and performance evaluation of this mechanism. Finally, we would like to mention a 6-DOF (1-PPRR/1-PPRRP)PR manipulator devised by Yang et al. [317] for intraocular surgery (Figure 11k). The 4-DOF parallel mechanism in this manipulator was actuated by piezoelectric drives. The authors developed a physical prototype of the robot and considered its control system in studies [323] and [324].

Most parallel mechanisms in the hybrid manipulators above had two DOFs and two branches. Scholars also proposed several architectures where the parallel part had three DOFs and three or more branches. For example, Tanev [318] introduced a 4-DOF (1-RRR/2-SPU)P manipulator with a spherical branch, which provides the RCM (Figure 11l). Subsequent works of the author focused on its stiffness [325] and singularities [326]. The RRR spherical chain was also used to provide the RCM in the parallel-serial manipulator considered by Phan et al. [319]. This chain was attached by an additional revolute joint to the 3-DOF Delta-type mechanism with linear drives (Figure 11m). The Delta mechanism also served as the basis for a 6-DOF hybrid manipulator with an RRP serial chain, proposed by Hong et al. [320] for neurosurgery (Figure 11n). However, to our knowledge, these three manipulators exist only as computer models. The final examples mentioned here are two hybrid robots developed for needle guidance. The first one is a PP(3-PRS) manipulator introduced by Chung et al. [321] (Figure 11o). The end-effector of this robot was equipped with a force-torque sensor and a handle for manual positioning during operations. The second example is an RRR(1-S/3-PSS) manipulator designed by Puglisi et al. [322] and based on a 3-DOF spherical parallel mechanism (Figure 11p). In their study, the authors analyzed the kinematics and performance of this mechanism and developed its physical prototype.

3.2.2. Manipulators for Non-minimally Invasive Surgery

Some parallel-serial manipulators developed for surgical operations do not have the RCM and are not intended for minimally invasive operations. For example, Ceccarelli et al. [327] proposed CaHyMan (Cassino Hybrid Manipulator) based on the 3-DOF 3-PaRS CaPaMan mentioned in Subsection 3.1.2. Here, the moving platform of CaPaMan is equipped with an RP serial chain (Figure 12a). The authors evaluated the stiffness of this manipulator and performed experiments in their subsequent studies [328] and [329]. Other CaPaMan-based parallel-serial surgical robots featured architectures with seven [330,331] and nine [332,333] DOFs, where the parallel mechanism was attached to 4-DOF SCARA and 6-DOF PUMA serial manipulators (Figure 12b and Figure 12c).

Feng et al. [334] introduced another surgical hybrid robot. This robot, designed for dental implant surgery, includes a 6-DOF Gough–Stewart platform attached to a PPPRR serial chain (Figure 12d). In their later works, the authors focused on the robot accuracy analysis [14,335] and calibration [336]. The last example is a Cheope manipulator designed by Tosi et al. [337]. It relies on a 4-DOF reconfigurable modular parallel mechanism with an RRP serial chain (Figure 12e). The authors considered various branch arrangements of this robot and analyzed its kinematics.

3.2.3. Manipulators for Fracture Reduction

Fracture reduction involves realigning broken bones, and scholars have developed various hybrid robotic systems for this purpose. The first group of manipulators is based on the 6-DOF Gough–Stewart platform. Raabe et al. [338] considered using this platform, attached to the linear guide, for the reduction of intra-articular joint fractures (Figure 13a). That idea was advanced by Dagnino et al. [339], who replaced the linear guide with a 4-DOF PPRR serial chain (Figure 13b). In papers [340] and [341], this system was applied to the reduction of complex knee fractures. In their other works [342,343], the authors considered a Gough–Stewart platform attached to the 6-DOF UR10 serial robot (Figure 13c). The latter was used for coarse positioning, while the platform served for precise movements.

Other examples of fracture reduction hybrid robots do not utilize the Gough–Stewart mechanism. Ye et al. [344] introduced a 6-DOF manipulator with a 4-DOF 2-PPRRP parallel mechanism attached to an RP serial chain (Figure 13d). The revolute joint of this chain was actuated by an RPR branch (not shown in the figure), whereas the end-effector included an auxiliary aligning mechanism. This manipulator was designed for fracture reduction of the femur shaft, and subsequent studies examined its kinematics [345,346] and control [347,348,349]. The second example is a 6-DOF manipulator proposed by Cai et al. [350] for pelvic fracture reduction and based on a 3-DOF 1-S/3-RRR spherical parallel mechanism (Figure 13e). In their paper, the authors focused on the kinematics and dynamics of this mechanism and presented its physical prototype.

Figure 13. Parallel-serial manipulators for fracture reduction: (a) P(6-UPS) [338]; (b) PPRR(6-UPS) [339]; (c) RRRRRR(6-UPS) [342]; (d) RP(2-PPRRP) [344]; (e) PPP(1-S/3-RRR) [350].

Figure 13. Parallel-serial manipulators for fracture reduction: (a) P(6-UPS) [338]; (b) PPRR(6-UPS) [339]; (c) RRRRRR(6-UPS) [342]; (d) RP(2-PPRRP) [344]; (e) PPP(1-S/3-RRR) [350].

3.2.4. Manipulators for Rehabilitation

Figure 14. Parallel-serial manipulators for rehabilitation: (a) (1-U/1-UPU/1-UPS)RR [351]; (b) (1-U/2-UPS)RRR [352]; (c) R(1-PU/2-SPS) [353]; (d) R(1-PU/2-CRS) [354]; (e) P(1-PR/1-PRP) [355].

Figure 14. Parallel-serial manipulators for rehabilitation: (a) (1-U/1-UPU/1-UPS)RR [351]; (b) (1-U/2-UPS)RRR [352]; (c) R(1-PU/2-SPS) [353]; (d) R(1-PU/2-CRS) [354]; (e) P(1-PR/1-PRP) [355].

Rehabilitation manipulators help patients restore the movements of their limbs. The literature review reveals several parallel-serial robots designed for these purposes, and they all were developed for the rehabilitation of lower limbs. For example, Shi et al. [351] proposed a 4-DOF manipulator based on a 2-DOF 1-U/1-UPU/1-UPS parallel mechanism (Figure 14a). The authors analyzed the mobility and kinematics of this robot in their study. Zhang et al. [352] developed a hybrid manipulator with a similar parallel mechanism and two serial chains, one for each leg of the patient (Figure 14b). In studies [356,357,358], the authors considered the robot kinematics and control and performed diverse experiments with its prototype. Among other examples are two 4-DOF ankle rehabilitation manipulators proposed by Li et al. [353] and Qu et al. [354]. Both manipulators have similar architectures: they include a 3-DOF parallel mechanism with a PU branch placed on the rotary platform; the only difference is in the two other branches (Figure 14c and Figure 14d). The final example is a 3-DOF manipulator designed by Mohanta et al. [355]. It is based on a 2-DOF 1-PR/1-PRP planar parallel mechanism that moves along a linear guide (Figure 14e). The authors’ studies focused on the robot kinematics, dynamics, and control [359].

3.2.5. Other Manipulators

This subsection will cover parallel-serial manipulators whose applications do not fit the categories discussed earlier. The first example is a robotic prosthetic arm designed by Wang et al. [360]. This manipulator includes a 2-DOF spherical parallel mechanism with two prismatic actuators and an RRR serial chain (Figure 15a). The authors’ study was devoted to the kinematic analysis of this robot. Larbi et al. [361] developed CochleRob, a 5-DOF parallel-serial robot for intracochlear navigation. The manipulator is based on a 3-DOF Delta robot placed on an RR spherical serial chain (Figure 15b). In papers [361] and [362], the authors studied the kinematics, dynamics, and different control strategies of CochleRob. Kucuk and Gungor [363] introduced a 9-DOF hybrid manipulator based on another familiar parallel mechanism—the Gough–Stewart platform, which was attached to a SCARA-type serial chain (Figure 15c). The authors focused on robot kinematic analysis but did not specify its medical application. One more kinematically redundant manipulator was presented by Singh et al. [26]. The parallel part of this 7-DOF manipulator represents a simple 1-DOF parallelogram linkage placed between two RRR serial chains (Figure 15d). The robot was applied as a haptic device for robot-assisted surgery, and the authors performed its kinematic analysis [364,365,366] and gravity balancing [367]. The final example is another medical assistive manipulator introduced in paper [73]. It includes a 2-DOF 1-PR/1-PRR planar parallel mechanism equipped with a PPR serial chain (Figure 15e). Works [368] and [369] performed a kinematic analysis of this robot, but its physical prototype has not been designed so far.

3.10. Other Applications

This subsection will discuss parallel-serial manipulators used in other applications not mentioned earlier. Thus, Wu et al. [484] proposed a 5-DOF spray-painting robot based on a 3-DOF planar parallel mechanism with two branches (Figure 24a). In paper [485], the authors analyzed the robot kinematics and dynamics and performed its dimensional synthesis, focusing on the parallel part. Wang et al. [486] considered another 5-DOF painting robot, which included a 1-U/2-SPU parallel mechanism and an RRR serial chain (Figure 24b), and studied its kinematics. Karim et al. [487] designed a 7-DOF PP(3-RPS)RR parallel-serial manipulator for high-power, high-repetition laser operations (Figure 24c). The authors developed a prototype of this device, and their later studies were devoted to its accuracy analysis [488,489] and control system [490]. An original pole-climbing parallel-serial robot was proposed by Vossoughi et al. [491]. This 4-DOF system included a 3-RPR planar parallel mechanism attached to a rotary base (Figure 24d). In later works, the authors focused on the dynamics [492], dimensional synthesis [493], design [494], and various applications [495] of the robot. Yan et al. [496] considered another exotic parallel-serial manipulator used for robotic dancing. It was based on a 4-DOF parallel mechanism attached to an RR serial chain (Figure 24e). In their study, the authors considered the robot kinematics and developed its prototype.

Finally, we would like to mention a few studies devoted to the theoretical analysis of some parallel-serial manipulators, without mentioning specific applications or developing physical prototypes. Chablat et al. [497,498] considered singularities and isoconditioning loci of a 3-DOF manipulator, which included a 2-DOF planar five-bar linkage (Figure 24f). Huang et al. [499] and Lee and Kim [500] studied the instantaneous kinematics of 6-DOF parallel-serial manipulators based on a 3-RPS parallel mechanism and an RRR serial chain (Figure 24g). The authors also performed a similar analysis for a hybrid manipulator with an RRP serial chain [501] (Figure 24h). Chen [502] considered the dynamics of a 9-DOF manipulator based on the Gough–Stewart platform equipped with an RRR serial chain (Figure 24i). Cha et al. [503] analyzed another kinematically redundant robot with the same parallel mechanism attached to a PPP serial chain (Figure 24j). The authors’ study was devoted to the robot kinematics and redundancy resolution.

Figure 24. Other parallel-serial manipulators for miscellaneous applications: (a) P(1-PRR/1-PRR)R [484]; (b) (1-U/2-SPU)RRR [486]; (c) PP(3-RPS)RR [487]; (d) R(3-RPR) [491]; (e) RR(1-RRRR/1-RRRRRP) [496]; (f) R(1-RR/1-RRR) [497]; (g) (3-RPS)RRR [499]; (h) (3-RPS)RRP [501]; (i) (6-UPS)RRR [502]; (j) PPP(6-UPS) [503].

Figure 24. Other parallel-serial manipulators for miscellaneous applications: (a) P(1-PRR/1-PRR)R [484]; (b) (1-U/2-SPU)RRR [486]; (c) PP(3-RPS)RR [487]; (d) R(3-RPR) [491]; (e) RR(1-RRRR/1-RRRRRP) [496]; (f) R(1-RR/1-RRR) [497]; (g) (3-RPS)RRR [499]; (h) (3-RPS)RRP [501]; (i) (6-UPS)RRR [502]; (j) PPP(6-UPS) [503].

4. Design and Analysis

5. Discussion

6. Conclusions

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