A new family of generalized parallel manipulators with configurable moving platforms
Introduction
A Conventional Parallel Manipulator (CPM) [1] is distinguished by connecting two platforms at the end of several serial limbs. Parallel manipulators with multiple closed-loops have fast speed, high stiffness, and considerable carrying abilities over the serial assemblies [2]. These advantages of performance for CPMs can lead to much more competent than the serial counterparts in some specific industrial applications.
For CPMs, the end moving platform is usually a rigid body (non-configurable platform) with kinematic joints fixed on one end-effector. Up to now, a large number of CPMs have been devised and built based on the most famous 6 degrees of freedom (DOFs) Stewart-Gough platform [3]. By employing the constraint synthesis method, Huang and Li [4] proposed the characteristics of structures and constraint of symmetrical 4/5-DOF parallel mechanisms. Fang and Tsai [5] synthesized a class of lower-mobility parallel manipulators with identical limbs. Based on the screw theory, Kong and Gosselin [6,7] performed the structure synthesis of 3-DOF translational and spherical parallel mechanisms. Zhang et al. [8], [9], [10] designed and analyzed a family of reconfigurable kinematic machines. Ge et al. [11] studied the innovative approach for the simultaneous type and dimensional synthesis of multi-DOFs manipulators. Xie et al. [12] conducted the structural synthesis of parallel manipulators with two translational motions (T) and one rotational motion (R). Ye et al. [13] designed a few symmetrical 2T2R parallel manipulators with identical limb structures.
However, the connected kinematic joints of GPMs are not demanded to be fixed on one end-effector to form the so-called configurable platforms. Then some unique characteristics can be obtained by the cooperation motion of the integrated end-effectors. As a result, this kind of mechanism can pick up objects with irregular shapes or large volumes. According to different arrangements, the non-rigid configurable platform may be further divided into serial open-loop linkages and closed-loop linkages. The serial open-loop configurable platforms are composed of single kinematic joints which are connected in the serial form [14]. The closed-loop configurable platforms consist of one closed-loop linkage, and the integrated end-effectors cooperate with each other [15]. Besides, the parallel manipulators with configurable platforms can realize a multipoint connection with the object or environment. These manipulators have the potential application to be utilized as micro-positioning or tactile feedback devices. Yi et al. [16] proposed a planar mechanism with a foldable parallelogram platform, which is the first research literature on parallel manipulators with configurable platforms. However, spatial manipulators are not involved in this study, and the concept of configurable platforms are not generalized. Afterward, Mohamed and Gosselin [15] put forward a general approach for calculating the DOFs of spatial parallel mechanisms with configurable platforms. However, this method is not subject to over-constraint parallel manipulators. Lambert et al. [17,18] analyzed the DOFs of over-constraint parallel manipulators with configurable platforms. Recently, Zeng and Ehmann [19] synthesized a new family of multi-loop parallel manipulators with deployable structures. Tian et al. [20] constructed a novel partially decoupled 3T1R parallel manipulator by using the threefold-symmetric Bricard linkage as middle platforms. Based on graph theory and screw theory, Hoevenaars et al. [21] synthesized two primary 3-DOF parallel mechanisms with configurable platforms. Jaime et al. [22] designed a parallel mechanism with two end-effectors through the planar closed-loop linkage. Lambert et al. [23] developed a new 7-DOF parallel haptic device by using a unique configurable platform. Jin et al. [14] designed a family of generalized parallel mechanisms with serial open-loop platforms. Besides, the idea of resorting to articulated moving platforms to improve rotational capacities has been demonstrated through some academic prototypes. Carricato [24] presented a fully isotropic 4-DOF parallel manipulator for Schoenflies motion. Sun et al. [25] designed some 1T3R parallel manipulators with articulated moving platforms by the helical pair. After integrating the configurable platforms with articulated moving platforms, the performance of the GPMs with configurable platforms can be highly improved [14].
Furthermore, because the mobility of the manipulators is more than the expected DOFs, parallel manipulators with configurable platforms are kinematically redundant manipulators [15]. The degree of redundancy is equal to the mobility of the configurable platforms. The additional redundant DOFs are utilized for reconfiguring the configurations of the moving platform itself. Besides, resulting from the feature of the nonrigid platforms, serial limbs are connected to the platform in limited quantities. With increasing the number of serial legs, the interference and constraint between the platform and limbs will be increased sharply. For parallel manipulators, to achieve better orientation performance and large workspace, the configurable platforms are expected to connect fewer legs as much as possible [26]. The number of active joints is equal to the dimension of the task space. And the active joints are installed on or next to the fixed base. Therefore, the multi-drive hybrid limbs are urgently desired to design full-controlled parallel manipulators with configurable platforms. The diagram of the topological structure for this kind of parallel manipulators is drawn in Fig. 1.
This paper, however, not oriented at CPMs, but aims at presenting a systematic method for designing parallel mechanisms with configurable platforms. A novel class of GPMs with configurable platforms is presented in this study. In Section 2, the closed-loop linkages are designed to form configurable platforms with integrated end-effectors. In Section 3, various serial limbs that exert different constraints on the end-effector are synthesized according to the screw theory. Then the multi-drive hybrid limbs are obtained through composing closed-loop chains and the serial limbs. To construct parallel manipulators with configurable platforms, the constraint synthesis method is analyzed. Afterward, a novel class of parallel manipulators with different motion patterns are synthesized. And the discussion of the driving schemes and the potential applications of the obtained manipulators are carried out. Finally, the conclusions are drawn in Section 6.
Section snippets
Design of configurable platforms
Different from rigid platforms of CPMs, the configurable platforms can be serial open-loop linkages or closed-loop linkages with integrated end-effectors. By reconfiguring the shapes of the nonrigid moving platforms, end-effectors can perform the cooperative movement. As a result, the tasks of grasping large objects with irregular shapes and performing parallel or intersecting motions can be achieved. For serial open-loop configurable platforms, two end-effectors are integrated by a single
Synthesis of limb structures
After devising configurable platforms, the serial legs performing various cooperative motions should be synthesized. The wrench systems of lower-mobility legs consist of constraint-couples and constraint-forces in accordance with the screw theory. Based on the number of constraints in the system, legs are categorized as six types indeed. By assembling appropriate links and joints on the ends of existing low-level legs (possessing more constraints), the high-level legs with fewer constraints are
Construction of parallel mechanisms
When constructing parallel manipulators, the structures of the configurable platforms need to be taken into consideration. With the number of limbs increasing, the interference and constraints among legs may be sharply magnified. Thus, the fewer limbs are expected to connect the end-effector as much as possible. And the number of connected limbs is restricted by the structures of the platforms. Therefore, two or three limbs are connected to the end-effectors in the proposed manipulators. The
Actuation
For full-controlled parallel mechanisms, the number of active joints is demanded to be equal to the dimension of outputs. When all active joints are locked, the dimension of the twist system for the end-effectors degenerates into null-space. Otherwise, the designed manipulator is uncontrollable. The mapping between output and input is demonstrated by the screw theory [6,40]. As the attitude and the position of the platform are determined in the workspace, at least one set of actuating
Conclusion
In this paper, a systematic approach for synthesizing parallel manipulators with configurable platforms has been proposed. Two classes of linkages with two or more integrated end-effectors have been designed, and five closed-loop configurable platforms have been proposed. Base on the screw theory, the serial limbs and the multi-drive hybrid limbs for constructing mechanisms have been enumerated. The derived limbs can provide various constraints (from none constraint to full constraints).
Declaration of Competing Interests
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
Acknowledgement
The 1st author would like to thank the financial support from the the China Postdoctoral Science Foundation (Grant No. 2019M660077). The 2nd author would like to thank the financial support from the Natural Sciences and Engineering Research Council of Canada (Grant No. RGPIN-2016-05030).
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