Elsevier

Mechanism and Machine Theory

Volume 120, February 2018, Pages 57-72
Mechanism and Machine Theory

Research paper
A class of novel 4-DOF and 5-DOF generalized parallel mechanisms with high performance

https://doi.org/10.1016/j.mechmachtheory.2017.09.015Get rights and content

Highlights

  • A new method for structural synthesis of the generalized parallel mechanisms is presented.

  • The proposed method provides a way to integrate the well-known close-loop kinematic chains into parallel mechanisms.

  • A class of 4-DOF and 5-DOF generalized parallel mechanisms is obtained.

  • The proposed mechanisms possess the motion advantages of the close-loop kinematic chains and the traditional parallel mechanisms.

Abstract

With the deepening and refinement of research, the traditional parallel mechanisms (PMs) have become increasingly hard to satisfy the demands of high rotational performance, decoupled motions, or some other specific motion properties. This paper focuses on the synthesis of a class of generalized parallel mechanisms (GPMs), which are capable of preserving the advantages and overcoming the shortcomings of the traditional PMs. Inspired by the closed-loop mechanisms with one or two dimensional high output performance and based on the characteristics of the set mapping and the group operations, a novel method about the synthesis of GPMs is proposed. By means of this method, a type of four degree of freedom (4-DOF) GPMs which contain 2T2R (T denotes a translational DOF and R represents a rotational DOF), 3T1R, and 1T3R categories are synthesized and further a kind of 5-DOF GPMs which are divided into 3T2R and 2T3R categories are obtained. The synthesis method is universal for the design of the GPMs and the proposed GPMs possess high performance because the articulated platforms are evolved from the well-known planar closed-loop linkage mechanisms.

Introduction

In general, a parallel mechanism is connected by a rigid platform and several parallel arranged limbs [1], [2], [3]. However, this acquiescent structural definition and design result in common defects that small workspace, lower rotational capability, lower global stiffness and lower task specificity for PMs. The generalized parallel mechanisms, which include the PMs with articulated moving platforms [4], [5], the PMs with coupling subchains [6], [7] and the PMs with configurable platforms [8], [9], can effectively solve the above problems. The PMs with articulated moving platforms are propitious to enlarge the rotational angles [10], [11], the PMs with coupling subchains contribute to improve the global stiffness [12] and the PMs with configurable platforms is suitable for specific tasks such as assembly and pick-and-place [13], [14]. More concretely, the articulated moving platform is an open-loop kinematic chain that can output one or more particular motions as long as connected with the parallel arranged limbs, whose displacements don't contain the open-loop kinematic chain's output motions. The coupling chain means that two parallel arranged limbs are connected by a kinematic chain so that they are no longer independent limbs of each other. The configurable platform generally denotes that the platform itself is a closed-loop kinematic chain, which has one or more inner DOF. Especially the GPMs with articulated platforms exhibit excellent rotational capability among the existing multi-dimension spatial mechanisms, such as the famous H-4 series [15], [16], [17] which is successfully applied to industry. Besides, the GPMs with articulated platforms not only have the advantage of larger rotational angles, but also possess the properties that flexible translational DOF, decoupling motions between rotations and translations [18]. However, most existing articulated platforms are constructed by experience and inspiration of the researchers, which causes the limited quantity and irregularity of the GPMs with articulated platforms. Thus finding the construction principle of the GPMs with articulated platforms and developing a synthesis method to design various constructions with common features are important research directions.

The planar closed-loop mechanisms are well researched and widely used in the uncomplicated industrial productions due to their high performance and lower mobility (less the three DOF) motion characteristics [19], [20], [21]. Such as the slider-crank mechanism can output whole cycle rotation if taking the crank as effector and can translate the input rotation into an output translation if taking the crank as driver and taking the slider as effector. Gosselin [22] proposed several singularity-free planar motion mechanisms with whole cycle rotational angles based on the traditional planar five-bar mechanisms. Ruiz-Torres [23] presented a novel 3-DOF translational PM CICABOT with large workspace based on two 5-bar mechanisms. Just because of the lower mobility of the planar closed-loop mechanism, their extension to the occasions that need spatial multi mobility (4–6 DOF) is limited, which results in a limited application in the complex multi-dimension high performance mechanisms. If the planar closed-loop kinematic chains are used to construct the articulated platforms in the GPMs in some way, the obtained GPMs can meet the requirement that spatial multi mobility motions of the end-effectors and meanwhile possess the high performance advantage of the planar closed-loop mechanisms.

The synthesis theories and methods for the traditional PMs are various and relatively mature, and a larger number of traditional PMs are obtained by these methods. It mainly includes the enumeration approach based on the general Chebyshev-Grübler-kutzbach mobility formula [24], the constraint synthesis method based on the screw theory [25], [26], the synthesis method based on the Lie group theory [27], [28]. However, there is no systematic synthesis method to apply the GPMs, even the existing methods mentioned above are seldom used to design the GMPs. As a result, development of a new theory or a new method by means of the existed mathematical theory for the GPMs’ structural synthesis is indispensable to design a series of high performance GPMs.

Hence, this paper focuses on developing a new method to synthesize the GPMs with articulated platforms by means of the set mapping and the group theory. This method is aimed at designing the GPMs whose articulated platforms are originated from the high performance closed-loop kinematic chains. This part is illustrated in Section 2. The closed-loop kinematic chains used in the generalized parallel mechanisms are normally the mature and common mechanisms or the evolutional configurations of them. Using the proposed synthesis method, a class of 4-DOF GPMs with specific high performance is obtained in Section 3. Similarly, a family of 5-DOF GPMs is proposed in Section 4. The proposed GPMs hold the both functions of the traditional PMs and the closed-loop kinematic chains. Finally, conclusion is drawn in Section 5.

Section snippets

A new method for structural synthesis

According to the Lie group theory, the set of 6-dimensional rigid motion can be endowed with the algebraic structure of a group, represented by {D} as Lie group. Further any motion of a rigid body can be described by a subset of {D}, which may be either a group, called a displacement subgroup (DSG) or a displacement submanifold (DSM). According to Hervé [29], {T(u)} denotes a linear translation parallel to u, and {R(N, u)} represents a rotation, whose rotational axis is determined by the unit

4-DOF generalized parallel mechanisms

A class of novel 4-DOF generalized parallel mechanisms can be synthesized using the above method. There are three kinds of 4-DOF parallel mechanisms, i.e., 2T2R PMs, 3T1R PMs and 1T3R PMs. In the process of PM synthesis, there are always faced with two difficulties. One is to design PMs with multi-dimensional rotations, in which at least one rotation is demanded to have large rotational angles. Another is to design larger than 3-DOF PMs which have to possess 3-D translational DOF. As a result,

5-DOF generalized parallel mechanisms

The 5-DOF mechanisms include the 2T3R category and the 3T3R type. As mentioned before, it is a relatively difficult process to design three translational DOF simultaneously and to construct rotational DOF greater than one because of the interference between different rotations. For the 3T2R mechanisms, if a closed-loop chain with 1T1R output displacements and two 2T input motions whose direction are both perpendicular to the output translations is developed, it just need to construct 2T1R

Conclusion

A methodology for the structural of the generalized parallel mechanisms with articulated moving platforms is presented. The construction principle is illustrated by combining the set mapping and the Lie group theory together. A series of articulated moving platform are obtained by the familiar planar closed-loop kinematic chains. The closed-loop kinematic chain is an excellent choice to design the generalized parallel mechanisms with high performance. The proposed GPMs remain the advantages of

Acknowledgments

The authors gratefully acknowledge the financial support of National Natural Science Foundation of China under grant No.51675037, No. 51475035, and No. 51505023.

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