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This paper presents a metamorphic parallel mechanism which can switch its motion between pure translation (3T) and pure rotation (3R). This feature stems from a reconfigurable Hooke (rT) joint of which one of the rotation axes can be altered freely. More than that, based on the reconfiguration of the rT joint, workspace of both 3T and 3R motion can...
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... 3-(rT)P(rT) metamorphic parallel mechanism consists of a base, a platform and three (rT)P(rT) limbs as in Fig. 3. The three limbs support the platform symmetrically around a reference circle of radius ra and connect to the base around a circle of radius rb. For the pure rotation case, the intersecting phase of the limb is used and all the JMR-15-1246-Gan-Page 6- radial axes of the rT joints in the three limbs intersect at point o as in Fig. 3 in ...
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... limbs as in Fig. 3. The three limbs support the platform symmetrically around a reference circle of radius ra and connect to the base around a circle of radius rb. For the pure rotation case, the intersecting phase of the limb is used and all the JMR-15-1246-Gan-Page 6- radial axes of the rT joints in the three limbs intersect at point o as in Fig. 3 in which the three limbs are numbered as limb 1, limb 2 and limb 3. Let Bi in the base denote the center of the base rT joint and Ai denote the center of the platform rT joint in the ith (i = 1, 2, 3) limb and A0 the geometric center of the platform. Locate a global coordinate frame oxyz at the rotation center o with z-axis ...
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... a platform coordinate frame o′x′y′z′ at point o′ with z′ axis perpendicular to the platform and y′ axis parallel to A1A0 as in Fig. 3(b), where o′ coincides with o and A0 is the center of mass of the platform. In each limb as in Fig.3, the radial axis of the base rT joint forms an angle αb with z-axis and is called the base- rT-joint angle, the radial axis of the platform-rT-joint forms an angle αa with z′-axis and is called the platform-rT- joint angle. Thus the base ...
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... a platform coordinate frame o′x′y′z′ at point o′ with z′ axis perpendicular to the platform and y′ axis parallel to A1A0 as in Fig. 3(b), where o′ coincides with o and A0 is the center of mass of the platform. In each limb as in Fig.3, the radial axis of the base rT joint forms an angle αb with z-axis and is called the base- rT-joint angle, the radial axis of the platform-rT-joint forms an angle αa with z′-axis and is called the platform-rT- joint angle. ...
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Citations
... Following this idea, a reconfigurable revolute (rR) joint was developed, with its axis of rotation lying in a fixed plane. Furthermore, a metamorphic parallel mechanism, of the 3-(rR)PS type, was designed to produce reconfigurable motions between a pure rotation and a 1T2R motion (one translation and two rotations) [9]. The extended reconfigurable revolute (rR) joint was proposed by Nurahmi et al. [10]. ...
Reconfigurable composite joints (RCJs) are essential elements in the design of reconfigurable mechanisms. One significant trend is to synthesize RCJs with pre-specified motion properties. This paper focuses on the general synthesis method for the design of RCJs based on motion decomposition and reconstruction (MDR). The overall concept of MDR targeting the design of RCJs is first introduced. Then, the concept and its application are described, including six steps: ( i ) determination of the main chain (MC); ( ii ) motion modeling of the MC; ( iii ) analysis and decomposition of the total motion of the MC; ( iv ) reconstruction of the chains with different submotions by means of auxiliary chains (ACs); ( v ) determination of the pertinent adjustable chain, and assembly of the MC, ACs, and the adjustable chain; and ( vi ) layout of the actuation scheme. Subsequently, three kinds of RCJs with different main chains are generated systematically by means of the concepts proposed herein. Finally, one reconfigurable parallel-kinematics machine (PKM) with one proposed RCJ in a limb is used as an example, which offers applications in the design of reconfigurable mechanisms. The proposed concept, MDR, is not only suitable for type synthesis of simple kinematic chains, but also potentially applicable to reconfigurable kinematic chains.
... The proposed error modeling method has the advantage of reflecting the physical meaning and influence factors of the error transmission process of each limb clearly, because it can identify the perturbation generated by the error sources of each limb separately. In addition, the defined accuracy indices based on the established error model are dimensionless and independent of the coordinate system, which are important advantages for performance evaluation and dimensional synthesis [38][39][40]. Therefore, the defined accuracy indices can be well used for accuracy evaluation and dimensional synthesis of translational parallel manipulators. ...
Accuracy is one of the most important properties for manipulators, and sensitivity analysis combined with tolerance allocation is usually used for ensuring their accuracy in the design stage. However, the improvement of tolerance grade is limited by manufacturing cost and processing technology level. For parallel manipulators, there are generally more joints than the serial ones, and the requirement for cost-efficient design is in urgent need. This paper focuses on error modeling, evaluating and improving the accuracy of parallel manipulators. Firstly, the error models based on motion/force transmissibility are established for translational parallel manipulators. The influence of motion/force transmissibility on theoretical accuracy is revealed. The result indicates that the position error of the parallel manipulator is inversely correlated with the output transmissibility of each limb. According to the established error models, the accuracy evaluation indices are proposed and used for accuracy optimization of the parallel manipulator via dimensional synthesis. The comparison before and after optimization shows that the optimized parallel manipulator has higher simulation accuracy. This work provides a new idea for the accuracy investigation of parallel manipulators.
... However, traditional parallel robots were designed to implement specific tasks thus have limit adaptability to demands of task variation due to their unique topological configuration. To address these challenges and bring in capacity for changing topological configuration without dismounting and reassembling, parallel robots with distinct function of reconfiguring their mobility [9,10] and motion mode [11] have been extensively investigated in recent years [12][13][14]. ...
Drawing inspiration from kirigami, a creative art of papercutting, this paper first present a simple crease pattern of a kirigami model. In terms of artimimetics which bridges the origami/kirigami art and mechanisms, the kinematic equivalent, an overconstrained 6R linkage, is extracted from the kirigami model. In terms of screw theory, constraint singularity induced transitory position and distinct closed-loop motion branches of the 6R linkage is revealed. Using the Bennett plano-spherical linkage as a closed-loop subchain of kinematic limbs, this paper then introduce a new reconfigurable parallel manipulator with three hybrid kinematic limbs. Each limb of the manipulator consists of a Bennett plano-spherical linkage and a R(RR) serial chain. Using a geometric approach, the constraints exerted on the platform by the hybrid limb are explored by analysing the motion-screw systems of the equivalent serial kinematic limb corresponding to each motion branch of the closed-loop subchain. Motion characteristics in each motion branch of the parallel manipulator are revealed. Inspired by origami-folding and inflatable actuators for soft robotics, this paper further presents a new design of inflatable bending actuator for changing motion branches of reconfigurable mechanisms. The conceptual design of the actuator is verified with a prototype fabricated using adhesive fabric and further application in reconfiguring a 3D printed foldable Bennett plano-spherical linkage.
... Over the past few decades, investigations on reconfigurable mechanisms have been carried out under different terms, e.g., kinematotropic mechanisms [1,2], metamorphic mechanisms [3,4,5], deployable mechanisms [6,7,8], and mechanisms with multiple operation modes [9,10]. The concept of operation modes was initially developed to drive attention to interpret five distinct 3-DOF motions performed by the DYMO (Double Y-Multi Operational) [11]. ...
... The reconfiguration is very useful for this application since we perform more motion types with less parts and motors as compared to the Stewart platform. All actuators of the 4-CRU mechanism are fixed on the ground, which will enable the mechanism to be more rigid 2 APPLICATION FOR 3D-PRINTING BUILDING 3 and agile, as compared to the serial robotic arm. Since we aim to print large parts, such as buildings, the ground carrying the workpiece cannot be oriented. ...
This paper aims to investigate the reconfiguration and self-motions of a 4-CRU parallel mechanism based on the mechanism geometric constraints. The targeted application of such mechanism in this research is for 3D-printing buildings of multi-directional nozzle as a new technology for constructing sustainable housing. By using primary decomposition, four geometric constraints are identified and the reconfiguration analysis is carried out in each of these. It reveals that each geometric constraint will have three distinct operation modes, namely Schoenflies mode, reversed Schoenflies mode and an additional mode. The additional mode can be either 4-DOF mode or it degenerates into 3-DOF mode, depending on the type of the geometric constraint. By taking into account the actuation and constraint singularities, the workspace of each operation mode is analysed and geometrically illustrated. It allows us to determine the regions in which the reconfiguration takes place. Furthermore, the moving-platform can still perform at least 1-DOF self-motion. It occurs at two specific actuated leg lengths. Demonstration of reconfiguration process and self-motions are also provided through a mock-up prototype.
... Kong et al. [5][6][7] presented a method for the type synthesis of parallel mechanisms with multiple operation modes. Gan et al. [8][9][10][11][12] proposed three kinds of metamorphic parallel mechanisms composed of three limbs with reconfigurable Hooke joints, and the unified kinematics analysis of a new 3rTPS metamorphic parallel mechanism were investigated. Zhang et al. [13][14][15] proposed a kind of metamorphic parallel mechanism extracted from origami fold and analyzed the evolutionary kinematic configuration changes of two metamorphic parallel mechanisms of 3SvPSv. ...
The current research of reconfigurable parallel mechanism mainly focuses on the construction of reconfigurable joints. Compared with the method of changing the mobility by physical locking joints, the geometric constraint has good controllability, and the constructed parallel mechanism has more configurations and wider application range. This paper presents a reconfigurable axis (rA) joint inspired and evolved from Rubik's Cubes, which have a unique feature of geometric and physical constraint of axes of joint. The effectiveness of the rA joint in the construction of the limb is analyzed, resulting in a change in mobility and topology of the parallel mechanism. The rA joint makes the angle among the three axes inside the groove changed arbitrarily. This change in mobility is completed by the case illustrated by a 3(rA)P(rA) reconfigurable parallel mechanism having variable mobility from 1 to 6 and having various special configurations including pure translations, pure rotations. The underlying principle of the metamorphosis of this rA joint is shown by investigating the dependence of the corresponding screw system comprising of line vectors, leading to evolution of the rA joint from two types of spherical joints to three types of variable Hooke joints and one revolute joint. The reconfigurable parallel mechanism alters its topology by rotating or locking the axis of rA joint to turn all limbs into different phases. The prototype of reconfigurable parallel mechanism is manufactured and all configurations are enumerated to verify the validity of the theoretical method by physical experiments.
... Therefore, it is very tough to obtain the global optimum dimensions and study the mapping relationships between various parameters, mechanisms, performances, modes, etc., considering all these concepts of unity of opposites. Similar problems can be seen in the researches by Gan [11,12], Yao [13], Ye and Zhang [14], etc. In this study, we propose the functional sequence optimization strategy based on the unidirectional configuration transition from landing to walking, and propose the kinematic decoupling optimization strategy to optimize the single leg and overall lander, and the execution mechanism and transmission mechanism respectively. ...
... Part 3: Optimum dimension design for the walking configuration of the ReLML, including both walking leg execution mechanism and multi-mode transmission mechanism. (12) Step 12: Identify the kinematic parameter design chains of the walking configuration; (13) Step 13: Derive walking performance indices and transmission performance indices; (14) Step 14: Identify walking constraint conditions and transmission constraint conditions. So far, the optimization design models of walking configuration containing the walking leg execution mechanism and multi-mode transmission mechanism have been derived; (15) Step 15: Employ the DSDRM-based PCbDM for the walking leg execution mechanism as a means of nondimensional optimization design, including establishing the physical model, plotting performance atlases, and selecting optimum parameters; (16) Step 16: Verify the applicability of the selected optimum parameters for the walking leg execution mechanism, by comparing different non-dimensional combinations and the corresponding comprehensive performances; (17) Step 17: Implementing Steps 15~16 for the multi-mode transmission mechanism, and obtain the optimum parameters; (18) Step 18: Identify the normalization factors by the inherited dimensions of landing configuration and dimensional performance indices; (19) Step 19: Calculate the dimensional parameters for the walking configuration, and obtain all real dimensions of the ReLML. ...
The reconfigurable legged mobile lander (ReLML) integrates both landing and walking modes, promising to be employed in the future extraterrestrial exploration as a counterpart of lander and rover. To tackle the optimization challenge that the ReLML possesses sixteen design parameters with multi-mode and complex mechanism topology: (1) this study firstly presents a systematic optimum dimension design strategy named after multimode synergistic optimization (MMSO), utilizing the functional sequences and kinematic decoupling to simplify the complex optimization issue into sub-issues of sub-mechanisms in sub-modes from landing to walking. After employing the design space dimensionalityreduction method (DSDRM), the metamorphic execution mechanism, overall lander, and multi-mode transmission mechanism are optimized successively; (2) then, four optimization models are established for the optimal comprehensive performance demands of landing and walking modes. To improve the performance chart-based design methodology (PCbDM) limiting at most four parameters, the DSDRM-based PCbDM is implemented for the global visualized optimization by four iterations of PCbDM. Finally, all global optimum dimensions of ReLML are identified. This work can also provide references for the dimensional synthesis of metamorphic mechanism, multi-mode mechanism, and reconfigurable mechanism.
... Based on these two kinds of metamorphic kinematic pairs, a variety of metamorphic parallel mechanisms are designed. Kong et al. [9] presented a three-degree-of-freedom parallel metamorphic mechanism with multiple motion modes based on a reconfigurable moving platform with lockable joints. Liu Jiangnan [10] proposed a new configuration design method of metamorphic mechanism based on constraint variation characteristics of metamorphic kinematic pairs. ...
This paper proposes the concept of full configuration state of metamorphic mechanism. Based on the concept, the configuration synthesis principle of metamorphic parallel mechanism is put forward. Firstly, a metamorphic parallel mechanism in full configuration state is synthesized, and then full configuration state evolves into a specific configuration state by increasing constraints or decreasing degrees of freedom. A reconfigurable moving platform based on the triple symmetric Bricard spatial closed-loop mechanism with a single degree of freedom is proposed. Based on this, a new method for switching motion configuration states of the metamorphic parallel mechanism is constructed. According to the configuration synthesis principle presented above, a novel metamorphic parallel mechanism that can switch between three- and four-degree-of-freedom is synthesized, and then the triple symmetric Bricard spatial closed-loop mechanism is used as the reconfigurable moving platform (that is, the reconfigurable foot of a walking robot) of the metamorphic mechanism, and thus, a novel metamorphic parallel leg mechanism is created. The screw theory is used to verify the degrees of freedom of the new type of metamorphic parallel leg. The proposed metamorphic parallel leg mechanism is expected to improve flexibility and adaptability of walking robots in unstructured environment.
... The transmissibility and constrainability are the main concerns in the performance evaluation of lower mobility PKMs. To evaluate the transmissibility, local transmission index (LTI) has been developed [35][36][37] and some valuable research has been presented [9,38]. Similarly, total constraint index (TCI) was established to evaluate the constraint performance of lower mobility PKMs [28]. ...
... Metamorphic parallel mechanisms have all the advantages of traditional parallel mechanisms in addition to the special ability to reconfigure their structures to obtain desired do f and motion type [8]. Based on the reconfigurable Hooke joint, named (rT) joint, various metamorphic parallel mechanisms have been synthesized in [9,10] and a general construction method using Screw Theory was introduced in [11]. A metamorphic parallel mechanism was designed by introducing a metamorphic kinematic pair in [12] and a variable-axis (vA) joint in [13]. ...
This paper focuses on the reconfiguration of a 3-(rR)PS metamorphic parallel mechanism based on complete workspace and operation mode analysis. The mechanism consists of three (rR)PS legs and each (rR) joint is composed of two perpendicular revolute joints. One of the (rR) joint axes can be reconfigured continuously which allows the mechanism to exhibit three distinct configurations. Initially, the constraint equations are derived by using algebraic geometry approach and the primary decomposition is computed for the three configurations. It reveals that the 3-(rR)PS metamorphic parallel mechanism can exhibit one up to two operation modes among three configurations. When the second axes of the three (rR) joints intersect at a finite point and not coplanar, the 3-(rR)PS metamorphic parallel mechanism has only one operation mode. If the second axes of the three (rR) joints are coplanar, the 3-(rR)PS metamorphic parallel mechanism has two operation modes. It is shown that both operation modes have the same motion type, namely 1T2R motion. However, to realize the same trajectories in both operation modes, the moving platform will have different orientations. Hence, the orientation workspaces of both operation modes are characterized and the axodes are used to compare the instantaneous motion of the moving platform when passing through the same trajectories. Based on these results, an identification approach is introduced to identify which operation mode a given mechanism pose belongs to and this provides a useful method for trajectory planning.
... The general construction approach based on Screw theory was presented in [12]. The reconfigurable Hooke joint (rT) [13], a metamorphic kinematic pair [14], a variable-axis joint (va) joint [15] were implemented to generate a number of metamorphic parallel mechanisms. ...
The 3-rRPS metamorphic parallel mechanism can change its configurations thanks to the reconfigurable (rR) joint. The analysis in this paper will focus on one specific configuration where the moving-platform is able to perform 2-dof coupled rotational motions and 1-dof translational motion, which is well-known as 1T2R motion. In this configuration, the mechanism has two types of operation modes, i.e. x0 = 0 and x3 = 0, which have been extensively studied by many researchers. However, the dynamic behaviours of the mechanism in those two operation modes have not been studied. Accordingly, this paper presents the dynamic analysis of the 3-rRPS metamorphic parallel mechanism in both operation modes based on the Instantaneous Screw Axis (ISA). The types of operation mode are initially characterized by means of Euler-Quaternion parameters. The time derivative of transformation matrix is performed in each operation mode and the ISA can be determined. By using the ISA, velocities and accelerations of all points on the moving-platform can be evaluated, which become the foundation of the dynamic analysis in this paper. This approach can be applied to parallel mechanisms having multiple operation modes of different mobility.
