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A SYNTHESIS APPROACH FOR RECONFIGURABLE REDUNDANT PARALLEL KINEMATICMECHANISMS

Hay Azulay, James K. Mills and Beno BenhabibDepartment of Mechanical and Industrial Engineering, University of Toronto, Toronto, Ontario, Canada

E-mail: [email protected], [email protected], [email protected]

Received November 2015, Accepted April 2016No. 15-CSME-115, E.I.C. Accession 3880

ABSTRACTThe design of a variety of novel Parallel Kinematic Mechanisms (PKMs) in the past three decades, andresearch into redundancy and reconfigurability have presented researchers with an opportunity to developreconfigurable PKMs. In this paper, a novel synthesis approach for Reconfigurable Redundant PKMs (RR-PKMs) is presented. The approach, motivated by the required reconfigurability, can help synthesize RR-PKMs that reconfigure into lower mobility sub-configurations, assembly/working modes, and sub-PKMs,without the disassembly of the structure. Implementing the proposed approach for the design of a 5-dofmachine tool, has led to the synthesis of a novel 3×RRPRS based RR-PKM that can reconfigure into fourPKMs.

Keywords: parallel kinematic mechanism; kinematic redundancy; reconfigurability; synthesis; lockablejoints.

SYNTHÈSE D’UN MÉCANISME CINÉMATIQUE PARALLÈLEREDONDANT RECONFIGURABLE

RÉSUMÉPendant les trois dernières décennies, la conception d’une nouvelle variété de mécanismes cinématiquesparallèles redondants et la recherche en redondance et reconfiguration a représenté pour les chercheursl’occasion de développer des mécanismes cinématiques parallèles reconfigurables. Dans le présent article,une nouvelle approche de synthèse d’un mécanisme cinématique parallèle redondant PKM reconfigurable(RR-PKM) est présentée. Cette approche motivée par la besoin de reconfiguration pourrait aider à synthétiserun mécanisme cinématique parallèle redondant reconfigurable en sous-configurations à mobilité plus faible,en modes assemblage/travail, et sous-mécanismes cinématiques parallèles sans le démontage de la structure.L’implantation de l’approche proposée pour la conception d’une machine-outil à 5 degrés de liberté à conduità un nouveau 3×RRPRS basé sur RR-PKM qui peut se reconfigurer en quatre PKMs.

Mots-clés : mécanisme cinématique parallèle; redondance cinématique; reconfiguration; synthèse; jointsverrouillables.

Transactions of the Canadian Society for Mechanical Engineering, Vol. 40, No. 3, 2016 419

1. INTRODUCTION

A variety of novel Parallel Kinematic Mechanisms (PKMs) developed over the past several decades havefacilitated the design of Redundant Reconfigurable PKMs (RR-PKMs). A common goal in reconfigurablePKM design has been to allow efficient topology modification according to a specified demand.

Contrary to the modular approach, which is acceptable in the robotic research field [1], in PKMs recon-figurability can be also obtained through kinematic redundancy. Finistauri and Xi [2] proposed a method foranalysis of PKMs that can reconfigure into lower mobility configurations. Gogu’s [3] Isogliden-TaRb is afamily of fully-isotropic PKMs that can reconfigure by locking actuators situated on the fixed base. Zhang etal. [4] presented a metamorphic mechanism that can satisfy different demands of lower limb rehabilitation.Grosch et al. [5] presented a class of reconfigurable PKMs that have a RRPS legs topology, where the firstrevolute joint can be locked/released on-line. The lockable joints allow manoeuvring of the platform basedon a probabilistic roadmap in order to avoid singularities and possible collisions. Herein, P,R,U , and S de-note prismatic, revolute, universal, and spherical joints, respectively. The topology of each PKM is denotedby the number of legs and the sequence of joints along the legs.

PKMs can also utilize geometrical reconfiguration. Zhang et al. [6] presented a three degree-of-freedom(dof) RR-PKM, in which the distance between the moving platform and the base can be adjusted usingvariable-length rods. A 5× SPU PKM, that can reconfigure by displacing its base attachments radiallywas depicted by Borras et al. [7]. Chen [8] optimized the dynamic-load carrying of a 3×PUPS PKM thatreconfigure via adjustment of joint locations along the base. Ye et al. [9] presented a family of reconfigurablePKMs with variable topology linkages. The PKMs are characterized by variations in joints positions andin actuators scheme that correspond with different motion modes. Carbonari and Callegari [10] designed aPKM with reconfigurable universal joints that allow the robot to vary its kinematics without changing jointssequence.

PKMs can also reconfigure between working/assembly modes. Herein, PKM configurations associatedwith the solutions to the direct/inverse kinematic models are denoted as assembly/working modes, respec-tively [11]. Budde et al. [11] and Schmitt et al. [12] presented reconfiguration processes of a planar PKMinto assembly modes. Campos et al. [13] presented the RRRRR DexTAR that can reconfigure into workingmodes in order to increase workspace coverage. Urízar et al. [14] studied the reconfiguration of a 3×SPS−SPKM into different assembly modes. Yi et al. [15] presented a 4-dof multi-mode PKM. The challenge insynthesizing a RR-PKM is to incorporate the required redundancy to support the desired reconfigurationprocesses. A synthesis methodology for PKMs based on evolutionary morphology was proposed by Gogu[16]. It was later implemented by Plitea et al. [17] in the design of a 3×PRRS PKM that can reconfigureinto lower mobility sub-configurations by coupling of joints in adjacent legs.

Several synthesis methods for RR-PKMs that can reconfigure into different modes of operation have beenreported. A mode of operation is a configuration, which is associated with specific tool-motion pattern, e.g.,pure rotational /translational motions. Kong et al. [18, 19] presented a synthesis method for PKMs that canbe reconfigured by changing the geometrical constraints between joints in adjacent legs and through the useof lockable joints to switch into different modes of operation.

Gao et al. [20] presented a synthesis method for PKMs that have special reconfigurable joints (rT), whichallows reorienting the joints rotation axes. Guo et al. [21] presented a synthesis method for variable topologyPKMs that is based on a genetic process. Zhao et al. [22] presented a method to enumerate possible actuationscheme of redundant PKMs.

The main challenge in synthesis of RR-PKMs is the design of mechanisms with the redundancy to supportthe required reconfigurability. Current methods do not propose a generic approach for the synthesis ofa single RR-PKM that can reconfigure into lower mobility sub-configurations, assembly/working modeconfigurations, and sub-PKMs that differ in topology. Furthermore, although the functionality of joints

420 Transactions of the Canadian Society for Mechanical Engineering, Vol. 40, No. 3, 2016

Fig. 1. A three-step RR-PKM synthesis process.

plays an important role in RR-PKMs, past synthesis methods have overlooked this aspect, i.e., determiningthe active, passive and lockable joints (joints that can switch from active to locked state).

Thus, in this paper, a novel synthesis approach for RR-PKMs that considers topology, level of redundancyand joint scheme is presented. The approach is demonstrated in detail via the synthesis of a novel 3×PRPRS RR-PKM, that for the best of the author’s knowledge is the first single architecture to reconfigureinto lower mobility sub-configurations, assembly/working mode configurations, and sub-PKMs that differin topology.

2. SYNTHESIS-METHODOLOGY DESCRIPTION

Synthesis of RR-PKMs, first and foremost, requires thorough knowledge of reconfigurability characteristicsof PKMs. RR-PKMs can achieve reconfigurability in three forms: Case 1 – Topological reconfiguration:Locking/unlocking joints to achieve a lower/higher mobility mechanism; Case 2 – Geometric reconfigura-tion: Adjusting the size/orientation of links and joints without rearranging the leg topology; and, Case 3 –Topological and geometric reconfiguration: Combining Cases 1 and 2 to reconfigure into assembly/workingmode configurations and into different sub-PKMs.

In order to synthesize RR-PKMs, a three-step process was developed (see Fig. 1). First, a set of PKMarchitectures with the required mobility, which can topologically reconfigure into lower mobility sub-configurations, is created. Second, PKMs are combined and redundant dof are incorporated to constructRR-PKM that can reconfigure into assembly/working modes. Third, the joint scheme of each RR-PKM isadjusted to allow reconfiguration into sub-PKMs that differ in topology.

2.1. Step 1 – Synthesis of PKMsIn this step, mechanisms with minimum required mobility are synthesized. A number of established synthe-sis methods for the creation of a library of PKMs have been documented in the literature [16]. Therefore,only the general outline of PKM synthesis is presented:

• Leg topologies with required connectivity are enumerated. Namely, we determine the order of rev-olute and prismatic joints along the leg, and their geometrical orientation with respect to each other.Connectivity of a leg is defined as the number of dof between the two sides of the leg [23].

• In the case that geometrical constraints result in kinematic redundancy, additional joints are addedto attain the required connectivity. For example, two revolute joints on the sides of a link that rotateabout the axis along the link are redundant. Therefore, another prismatic joint, or a revolute joint thatrotates about a diffrent axis, should be incorporated.

• Legs with identical connectivity are combened into closed-loop mechanism with required mobility.Considering the motion space, ρ , the number of links n, the number of joints p, the degree of motionof a joint, gi, and the redundant constraints, g j, mobitity is defined by

M = ρ · (n− p−1)+∑gi −g j. (1)


Fig. 2. Synthesis process of 3-dof PKMs in Step 1.

An illustrative example is presented in Fig. 2, where the objective is to synthesize 3-dof PKMs. Themechanisms are synthesized from a library of building blocks shown at the center of the figure. The firstcircle represents legs with connectivity of three, which are constructed from the building blocks. The secondcircle represents 3-dof PKMs, which are assembled from legs in the first circle and bases and platforms fromthe library of building blocks.

2.2. Step 2 – Combination of assembly/working mode configurations into a RR-PKMIn Step 2, RR-PKMs that can reconfigure to assembly/working modes configurations without the disas-sembly of the structure are synthesized. The topologies of assembly/working modes of a single PKM areidentical. Hence, the approach chosen in the synthesis of each RR-PKM is to combine, from the set that wascreated in Step 1, PKMs that are exactly alike in topology. Each PKM is associated with a specific assemblymode. Therefore, given identical topology PKMs, their singularities, that separate the assembly/workingmodes of the RR-PKM, are identified. Then, redundant dof to avoid the singular configurations are incor-porated, based on predetermined guidelines. The guidelines are based on the understanding of geometricalconditions that result in singularities.

PKM Jacobian defines the relationship between active joints velocities Q and tool velocity X

JqQ+JxX = 0, (2)

where Jq and Jx are the joint-space and task-space Jacobian matrices, respectively. Accordingly, three typesof kinematic singularities exist: Type 1 – Jq is singular: in this singularity there is a non-zero velocity vector,Q, for which the platform does not move; Type 2 – Jx is singular: in this singularity, there is a non-zero toolvelocity, X, for which the joint velocities are zero; Type 3 – both Jq and Jx are singular. In order to assurethat Type 3 singularity increases mobility, the velocity Jacobian has to be analyzed [24, 25].

In order to develop guidelines for combining identical-topology PKMs into a single RR-PKM, severalexamples of typical singularities, and approaches to avoid them, are presented. It is noted that otherguidelines may be added based on other singularities:


Fig. 3. Two working modes in PKMs with: (a1) RRR legs, (b2) PRR legs. The continuous lines represent the firstconfiguration and the dashed lines the second configuration, respectively.

Example 1: In legs with more than two joints, where there exist a revolute joint along the leg, singularityoccurs when the links on the two sides of the revolute joint are aligned. For example, Jx and Jq of a PKMwith RRR legs, shown in Fig. 3(a1), are derived as follows:

Jx = [bi k · (ci ×bi) Jq = [k · (ai ×bi)], (3)

where ai, bi and ci are the vectors for links along the ith leg, and k is the unit vector in the directionnormal to the platform plane. A Type-1 singularity, which is associated with the inverse-kinematic solution,occurs when ai and bi are parallel, and it divides between two working modes of PKMs with RRR legs, seeFig. 3(a1). This singularity can be avoided by replacing a passive revolute joint by a lockable joint, whichallows the PKM to switch between the working-mode configurations [12]. For example, locking the firstrevolute joint, Ai, along the ith leg (see Fig. 3(a2)), changes the leg topology into RR. Thus, eliminatingthe singular configuration in which the three joints, Ai, Bi and Ci, are along the same line. With the newtopology, link bi can move in proximity to and swing across the configuration, which is no longer singular.

Example 2: Type-1 singularity of PKMs with PRR legs is shown in Fig. 3(b1). Occasionally, reconfigu-ration into a different working/assembly mode may require planning, so that the transition is not limitedby geometric constraints. The fix connection of the leg to the base limits the transition of the PKM intoworking modes. Reconfiguration between the working modes can be obtained by adding a lockable revolutejoint between the base and the prismatic joint whose orientation needs to be adjusted (Fig. 3(b2)). Thelockable joint will be unlocked before switching, and locked after the first link is reoriented. Here, lockablejoints are denoted by the superscript L.

Examples 3 and 4: Singularity in three- and six-leg mechanisms, with spherical joints connecting the legsto the platform [26, 27], is demonstrated here via the 6-dof UofT PKM shown in Fig. 4. The topology ofthis PKM is 3×PPRS, where the first actuated prismatic joint, M1, moves along a circular rail. The secondactuator, M2, is mounted on M1 and moves radially. Furthermore, each leg includes a passive revolute jointand a spherical passive joint.

The loop-closure equation of the ith leg in Fig. 4 can be expressed in [28] as follows:

OAi +AiBi = OT +T Bi. (4)

Differentiating Eq. (4) with respect to time, and eliminating the contribution of the passive joints, yields theplatform’s angular velocity term, ω , where

˙T Bi = (bi × fi) ·ω. (5)


Fig. 4. The UofT PKM.

Fig. 5. Singularity avoidance in 3×PPRS PKMs: (a) singular configuration (co-planar planes), (b) added redundancyto avoid the singularity, (c) singular configuration (three planes coincide at the center of the platform), and (d) addedredundancy to avoid the singularity.

Above, fi denotes the unit vector of T Bi and bi denotes the unit vector of AlBl . In a configuration in whichbi and fi are parallel, ˙T Bi is equal to zero, and the Jacobian Jx is singular.

In [27], the general condition for this Type-2 singularity was identified for three-leg 6-dof PKMs. Thesingularity occurs when the platform plane and a leg are co-planar, as shown in Fig. 5(a). The platform planeis defined by the spherical-joints’ locations, and the plane comprising a single leg is defined by its respectivespherical-joint’s location and the zero-pitch screw of the revolute joint (the joint’s axis of rotation). Thissingularity can be avoided by incorporating a redundant joint into the leg. The redundant joint allowschanging the plane comprising the leg, so that it is not co-planar with the platform plane; see Fig. 5(b).


Fig. 6. Leg arrangements for different modes of motion.

Singularity in 3×PRPS and 3×PRPS PKMs may also occur when the planes of the legs intersect atthe center point of a joint, or at the center of the platform (Fig. 5(c)). This singularity can be avoided byincorporating a redundant joint into a leg, such, that the new plane which is defined by the redundant joint,and the planes of the other legs, intersect at a point that does not lead to a singular configuration (Fig. 5(d)).

In the last example, instead of adding joints to avoid singularity, they are added to change the geometricrelation between joints along the legs, to allow reconfiguration between tool-motion modes.

Example 5: A PKM whose revolute-joint axes intersect at a common point is limited to rotational-toolmotion, Fig. 6(a) [29]. The tool can move along a specific axis when the joint axes in each leg are (i) parallelto each other, but (ii) not parallel to the joint axes of the other legs (Fig. 6(b)), i.e., per the linear motion ofthe Sarrus mechanism along its axis of symmetry.

In PKMs with RRR legs, switching between tool-motion modes can be obtained by incorporating lockablerevolute joints for reorienting the joints’ axes. Thus, for example, two lockable joints can be added beforethe second revolute joint, and another two lockable joints added before the third revolute joint (Figs. 6(c1)and (c2)). The topology of the adjustable leg is now RRLRLRRLRLR and it can switch between the twomodes of motion mentioned above.

An example of a PKM that comprises revolute and universal joints (where a universal joint can be substi-tuted by two revolute joints), and that can reconfigure between different modes of motions is discussed in[18, 19]. The motivation for such a mechanism design is to have (i) the ability to achieve different modesof motion, and (ii) the ability to enhance performance by locking redundant dof that are not required for thedesired mode of motion.

2.3. Step 3 – Combine PKMs that Differ in Topology into a RR-PKMIn Step 3, the objective is to adjust the actuator scheme so that the RR-PKM can reconfigure into sub-PKMs,which differ from the assembly/working modes in topology. The sub-PKMs should be sub-topologies of theRR-PKM, and they are selected from the set of mechanisms that was created in Step 1. Since in this step,only the joint scheme is adjusted, the sub-PKMs should have the following characteristics:

• PKMs with a number of legs that is equal to the RR-PKM’s number of legs.

• Legs topology that can be obtained by locking/unlocking/reorienting joints of the RR-PKM synthe-sized in Step 2.

• Prismatic joints that move along the same path (linear, circular, etc.) as the prismatic joints of theRR-PKM synthesized in Step 2.


Table 1. Three- and six-leg PKMs.Source Name Topology dof Motion spaceJongwon et al. [33] Eclipse PKM 3×PPRSAlizade et al. [34] Alizade PKM 3×PRPSAzulay et al. [35] UofT PKM 3×PPRSGlozman and Shoham [36] Glozman PKM 3×PRRSPlitea et al. [17] Recrob 3×PRRS 6 SpatialByun and Cho [37] 3×PRRPChen [8] 3×PRPSYu et al. [38] Hexaglide, Linapod, HexaM 6×SPSMuruganandam and Pugazhenthi [39] Hexapod 6×SPS

The guidelines to determine the joint scheme that will allow the RR-PKM to reconfigure into severalsub-PKMs are:

• An active joint in a sub-PKM has to be active in the RR-PKM.

• A joint that switches from locked state to passive state for reconfiguration has to be lockable.

• In case of a joint that needs to switch from a passive state to an active state, two different RR-PKMvariants will be synthesized. In the first RR-PKM, the joint will be passive, and in the second variant,the joint will be actuated.

3. A SYNTHESIS TEST CASE

Example applications for PKMs include medical [30] and space [31] industries, as well as machining [32].Herein, we present a synthesis test case of a RR-PKM based tool-holder that is capable of 3D machining.

3.1. Synthesis Process – Step 1In this step, a set of PKMs topologies is created. Since tool-motions in PKMs are coupled, 6-dof PKMsare considered here for a 5-axis tool-holder. Furthermore, in order to demonstrate that topologies of knownPKMs can be combined into a single RR-PKM, the following example focuses on a set of three- and six-isomorphic-leg PKM topologies (Table 1).

n-dof (2 ≤ n ≤ 6) PKMs can be topologically reconfigured into lower mobility sub-configurations byapplying the holding-force of an actuator to restrict their tool’s motion. For example, sub-configurationsof the 6-dof Eclipse PKM are shown in Fig. 7. The topology of this PKM is depicted as follows: the firstactuator in each leg, M1, moves along a circular rail, and the second actuator, M2, which is mounted onM1 moves vertically. The legs also include a passive revolute joint and a passive spherical joint. In sub-configuration 7, all the actuators are active. In sub-configurations 1–3, a curvilinear prismatic joint in oneof the legs is locked, and in sub-configuration 4–6, one vertical prismatic joint is locked. The position of thelocked joint along a leg is circled.

The advantage of lower mobility sub-configurations is higher stiffness compared to the full mobilityconfigurations. However, in some cases, kinematic redundancy can be utilized to optimize the poses of thePKM along a given trajectory for desired performance criteria, such as stiffness [40]. Thus, a configurationshould be selected after the performance of the different variants are analyzed.

3.2. Synthesis Process – Step 2In Step 2, an RR-PKM based tool-holder that can be reconfigured into assembly/working mode configura-tions is synthesized. As can be noted from Table 1, the Eclipse and the UofT PKM are based on identical


Fig. 7. Sub-configurations of the Eclipse PKM.

Fig. 8. PKM architectures: (a) the Eclipse 3×PPRS [33], (b) the UofT PKM 3×PPRS [35].

3× PPRS topologies, and their prismatic base joints move along circular paths. Thus, they are assem-bly/working modes of a single PKM (Fig. 8).

In order to combine the two PKMs into a single RR-PKM, the first prismatic joint should reorient. Thus,a lockable revolute joint is incorporated to each leg of the 3×PPRS PKM before the second prismatic joint,and the equivalent RR-PKM joint scheme is 3×PRLPRS. The lockable revolute joints allow the first link ineach leg to rotate from radial position (Fig. 9(a)), to vertical position (Fig. 9(d)), where the angle χ , changesfrom 0◦ to 90◦ (Fig. 9(c)).

Reconfiguration into a different working/assembly mode requires planning, so that the transition is notlimited by geometric constraints and the RR-PKM does not get into singularity. For example, during thetransition from the configuration shown in Fig. 9(a) to the configuration shown in Fig. 9(c), the mechanismgoes through a singular posture where the links’ axes are orthogonal to the normal of the platform. Thissingularity can be avoided by locking the second revolute joint during the reconfiguration process [12].Hence, the joint scheme of the RR-PKM after Step 2 is 3×PRLPRLS.

3.3. Synthesis Process – Step 3In Step 3, the joint scheme of the RR-PKM that was synthesized in Step 2 is adjusted, such that it can bereconfigured into sub-PKMs that differ in topology. Comparing the topologies in Table 1, with the topologyof the 3×PRLPRLS RR-PKM, it can be noted that it lists two sub-topologies of the RR-PKM. These sub-topologies are based on 3×PXXS, where the symbol X denotes a joint that is prismatic or revolute.

The first PKM, which is associated with these sub-topologies, is the 3×PRPS Alizade PKM (Fig. 10(b))


Fig. 9. RR-PKM reconfiguration from (a) the UofT PKM to (d) the Eclipse.

Fig. 10. PKM architectures: (a) the Glozman PKM 3×PRRS [36], (b) the Alizade PKM 3×PRPS [34].

[35]. This PKM is constructed from a prismatic actuator, M1 that moves along a circular rail, a passiverevolute joint, a prismatic actuator, M2, and a spherical joint that connects the leg to the platform. Thesecond PKM is the 3×PRRS Glozman PKM, shown in Fig. 10(a). The legs of the Glozman PKM areconstructed from a prismatic actuator, M1 that moves along a circular rail, a passive revolute joint, a rotaryactuator, M2, and a spherical joint that connects the leg to the platform.

In order for the Eclipse/UofT PKM to reconfigure into the Alizade PKM and vice versa, both the secondand third revolute joints along each leg of the 3×PRLPRLS RR-PKM should be lockable. The RR-PKMjoint scheme supports that: in the Eclipse/UofT PKM, the second revolute joint is locked and the thirdrevolute joint is unlocked; in the Alizade PKM, the second revolute joint is unlocked and the third revolutejoint is locked. Reconfiguration from the UofT PKM to the Alizade PKM is shown in Figs. 11(a)–(e). TheGlozman PKM is a sub-topology of the 3×PRLPRLS RR-PKM, but its joint scheme is different. Replacingthe second revolute lockable joint in each leg with an active joint, to get a 3×PRLPRS topology, allows theRR-PKM to reconfigure into the Glozman PKM.


Fig. 11. RR-PKM reconfiguration from (a) the UofT PKM to the (e) the Alizade PKM.

4. CONCLUSIONS

A novel synthesis method for RR-PKMs, which is motivated by reconfiguration requirements, is presentedin this paper. The method adapts the RR-PKM structure to support the desired reconfigurability cases,and it can, through a sequential process, obtain reconfiguration into lower mobility sub-configurations, as-sembly/working modes, and PKMs that differ in topology. In the synthesis process, redundancy and jointscheme of the RR-PKM are utilized for avoiding singularities, and for obtaining the required tool motions.

The proposed approach is illustrated through the synthesis of a 3× PRPRS RR-PKM that can obtainthe different reconfiguration cases in a single architecture. In addition, the importance of joint scheme forreconfiguration is demonstrated.

ACKNOWLEDGEMENT

The authors thank the NSERC Strategic Network-CANRIMT and Promation Ltd. for funding this research.

REFERENCES

1. Benhabib, B. and Dai, M.Q., “Mechanical design of a modular robot for industrial applications”, Journal ofManufacturing Systems, Vol. 10, pp. 297–306, 1991.

2. Finistauri, A.D. and Xi, F., “Reconfiguration analysis of a fully reconfigurable parallel robot”, Journal of Mech-anisms and Robotics, pp. 0410021–04100218, 2013.

3. Gogu, G., “Isogliden-TaRb: A family of up to five axes reconfigurable and maximally regular parallel kinematicmachines”, Paper presented at the International Conference on Smart Machining Systems, Gaithersburg, 2007.

4. Zhang, W., Zhang, S., Ceccarelli, M. and Shi., D., “Design and kinematic analysis of a novel metamorphicmechanism for lower limb rehabilitation”, in Advances in Reconfigurable Mechanisms and Robots II, pp. 545–558, Springer International Publishing, 2016.

5. Grosch, P., Di Gregorio, R., Lopez, J. and Thomas, F., “Motion planning for a novel reconfigurable parallelmanipulator with lockable revolute joints”, Paper presented at the IEEE International Conference on Roboticsand Automation (ICRA), 2010.

6. Zhang, D. and Shi, Q., “Novel design and analysis of a reconfigurable parallel manipulator using variable geom-etry approach”, in Practical Applications of Intelligent Systems, Shanghai, China, pp. 447–457, 2012.


7. Borras, J., Thomas, F., Ottaviano, E. and Ceccarelli, M., “A reconfigurable 5-dof 5-SPU parallel platform”, inProceedings ASME/IFToMM International Conference on Reconfigurable Mechanisms and Robots, pp. 617–623, 2009.

8. Chen, C.T., “Reconfiguration of a parallel kinematic manipulator for the maximum dynamic load-carrying ca-pacity”, Mechanism and Machine Theory, Vol. 54, pp. 62–75, 2012.

9. Ye, W., Fang, Y., Zhang, K. and Guo, S., “A new family of reconfigurable parallel mechanisms with diamondkinematotropic chain”, Mechanism and Machine Theory, Vol. 74, pp. 1–9, 2014.

10. Carbonari, L. and Callegari, M., “The kinematotropic 3-CPU parallel robot: Analysis of mobility and reconfig-urability aspects”, Paper presented at the Conference on Latest Advances in Robot Kinematics, 2012.

11. Budde, C., Helm, M., Last, P., Raatz, A. and Hesselbach, J., “Configuration switching for workspace enlarge-ment”, in Robotic Systems for Handling and Assembly, D. Sch’utz and F. Wahl (Eds.), Vol. 67, pp. 175–189,Springer Berlin/Heidelberg, 2011.

12. Schmitt, J., Inkermann, D., Raatz, A., Hesselbach, J. and Vietor, T., “Dynamic reconfiguration of parallel mech-anisms”, in New Trends in Mechanism Science: Analysis and Design, D. Pisla et al. (Eds.), Springer, Dordrecht,2011.

13. Campos, L., Bourbonnais, F., Bonev, I.A. and Bigras, P., “Development of a five-bar parallel robot withlarge workspace”, in Proceedings of the ASME 2010 International Design Engineering Technical Confer-ences & Computers and Information in Engineering Conference (IDETC/CIE), Montreal, Quebec, Canada,2010.

14. Urízar, M., Petuya, V., Amezua, E. and Hernández, A., “Characterizing the configuration space of the 3-SPS-Sspatial orientation parallel manipulator”, Meccanica, pp. 1–14, 2013.

15. Yi, B.-J., Kim, S.M., Kwak, H.K. and Kim, W., “Multi-task oriented design of an asymmetric 3T1R type 4-DOFparallel mechanism”, P I Mech Eng C-J Mec, Vol. 227, pp. 2236–2255, 2013.

16. Gogu, G., Structural Synthesis of Parallel Robots Part 1: Methodology, Vol. 149. Springer, Dordrecht, 2008.17. Plitea, N., Lese, D., Pisla, D. and Vaida, C., “Structural design and kinematics of a new parallel reconfigurable

robot”, Robot Cim-Int Manf, Vol. 29, pp. 219–235, 2013.18. Kong, X., Gosselin, C.M. and Richard, P.-L., “Type synthesis of parallel mechanisms with multiple operation

modes”, Journal of Mechanical Design, Vol. 129, pp. 595–601, 2007.19. Kong, X. and Jin, Y., “Type Synthesis of 3-DOF multi-mode translational/spherical parallel mechanisms with

lockable joints”, Mechanism and Machine Theory, Vol. 96, Part 2, pp. 323–333, 2016.20. Gan, D., Dai, J.S. and Caldwell, D.G., “Constraint-based limb synthesis and mobility-change-aimed mechanism

construction”, Journal of Mechanical Design, Vol. 133, pp. 051001–9, 2011.21. Guo, Z., Wang, K., Xu, Z. and Qi, H., “Topological design and genetic synthesis of the variable topology parallel

mechanisms”, Paper presented at the ASME/IFToMM International Conference on Reconfigurable Mechanismsand Robots, 2009.

22. Zhao, J.S., Chu, F., Feng, Z.J. and Dai, J.S., “Actuation schemes of a spatial 3-PPRR parallel mechanism”, P IMech Eng C-J Mec, Vol. 226, pp. 228–241, 2012.

23. Shoham, M. and Roth, B., “Connectivity in open and closed loop robotic mechanisms”, Mechanism and MachineTheory, Vol. 32, pp. 279–293, 1997.

24. Zlatanov, D., Fenton, R. and Benhabib, B., “Analysis of the instantaneous kinematics and singular configurationsof hybrid-chain manipulators”, in Proceedings ASME 23rd Biennial Mechanisms Conference, Minneapolis, MN,pp. 467–476, 1994.

25. Altuzarra, O., Pinto, C., Avilés, R. and Hernández, A., “A practical procedure to analyse singular configurationsin closed kinematic chains”, IEEE Transactions on Robotics, Vol. 20, pp. 929–940, 2004.

26. Ben-Horin, P. and Shoham, M., “Singularity of Gough–Stewart platforms with collinear joints”, Paper presentedat the 12th IFToMM World Congress, Besançon, France, 2007.

27. Ben-Horin, P. and Shoham, M., “Singularity condition of six-degree-of-freedom three-legged parallel robotsbased on grassmann-cayley algebra”, IEEE Transactions on Robotics, Vol. 22, pp. 577–590, 2006.

28. Tsai, L., Robot Analysis: The Mechanics of Serial and Parallel Manipulators, John Wiley and Sons, New York,1999.

29. Fang, Y.F. and Tsai, L.W., “Structure synthesis of a class of 4-dof and 5-dof parallel manipulators with identicallimb structures”, International Journal on Robotics, Vol. 21, pp. 799–810, 2002.


30. Bourges, J.L., Hubschman, J.P., Wilson, J., Prince, S., Tsao, T.C. and Schwartz, S., “Assessment of a hexapodsurgical system for robotic micro-macro manipulations in ocular surgery”, Ophthalmic Research, Vol. 46, pp. 25–30, 2011.

31. Valasek, M., Zicha, J., Karasek, M. and Hudec, R., “Hexasphere – Redundantly actuated parallel sphericalmechanism as a new concept of agile telescope”, Advances in Astronomy, Vol. 2010, pp. 1–6, 2010.

32. AGIETRON micro nano. Available from http://www.gfac.com/, April 2, 2011.33. Jongwon, K., Chongwoo, P., Joong, R.S., Jinwook, K., Chul, H.J., Changbeom, P. and Iurascu, C.C., “Design

and analysis of a redundantly actuated parallel mechanism for rapid machining”, IEEE Journal of Robotics andAutomation, Vol. 17, pp. 423–434, 2001.

34. Alizade, R.I., Tagiyev, N.R. and Duffy, J., “A forward and reverse displacement analysis of a 6-dof in-parallelmanipulator”, Mechanism and Machine Theory, Vol. 29, pp. 115–124, 1994.

35. Azulay, H., Mahmoodi, M., Zhao, R., Mills, J.K. and Benhabib, B., “Comparative analysis of a new 3×PPRSparallel kinematic mechanism”, Robot Cim-Int Manf, Vol. 30, pp. 369–378, 2014.

36. Glozman, D. and Shoham, M., “Novel 6-dof parallel manipulator with large workspace”, Robotica, Vol. 27,pp. 891–895, 2009.

37. Byun, Y.K. and Cho, H.S., “Analysis of a novel 6-DOF, 3-PPSP parallel manipulator”, International JournalRobotics Research, Vol. 16, pp. 859–872, 1997.

38. Yu, W.-J., Huang, C.-F. and Chieng, W.-H., “Workspace and dexterity analyses of the Delta Hexaglide platform”,Journal of Robotics and Mechatronics, Vol. 20, pp. 7–17, 2007.

39. Muruganandam, S. and Pugazhenthi, S., “Selection of optimal machining parameters for hexapod machine tool”,International Journal of Advanced Manufacturing Technology, Vol. 46, pp. 801–810, 2010.

40. Azulay, H., Mills, J.K. and Benhabib, B., “A multi-tier design methodology for reconfigurable milling ma-chines”, Journal of Manufacturing Science and Engineering, Vol. 136, pp. 041007 1–10, 2014.


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