Zhen Huang

In this paper, a novel 3-UPU (P and U stand for prismatic and universal joints, respectively) parallel mechanism (PM) and its variant PM are proposed. Both of them have two rotational and one translational (2R1T) degrees of freedom (DOFs) without involving any parasitic motion. Mobility analysis shows that the three constraint forces provided by three limbs of the mechanism are located on the same plane and the mobile platform can translate perpendicular to this plane and rotate around any axis on it. Analysis of the mechanism’s motion characteristics demonstrates that the mobile platform outputs either pure rotation or pure translation. Moreover, the rotational axis can be fixed during the rotation process, which means no parasitic motion is involved. The causes of the motion characteristics are analyzed by the combination of an overall Jacobian matrix, a statistical method, and a geometric method. The PMs only need to translate or rotate once to move from the initial configuration to the final configuration, which allows for easy control of speeds. The relationship between mechanism parameters and singularity is analyzed. A speed control method for the PMs is proposed and a prototype is designed and made. Experiments are conducted to verify the determined motion characteristics, the speed control method, and the singularity analysis.

The mobility(or degree of freedom) analysis of planar mechanisms is traditionally calculated using the Grübler–Kutzbach formula. However, this method often fails in practice due to overconstraint, which is a core problem in all mobility analysis. Analyzing the cause of overconstraint, it is presented that overconstraint in closed-loop mechanisms can be recognized by analyzing the relative movements of the two elements in a rigidity re-closure. A solution to determine the overconstraint in multiloop mechanisms is also proposed. In this method, each loop is opened and the overconstraint can be calculated when the loop is reclosed. A mobility analysis must begin by determining the overconstraint. However, given that most planar mechanisms do not have any overconstraint, it is important to identify rapidly whether overconstraint exists in a mechanism. This paper proposes a concise technique to determine the existence of overconstraint based on the concept of “Assur groups”. To simplify the process of mobility analysis, three new concepts and four relevant theories are introduced. In this paper, the proposed methodology is applied to several types of planar mechanisms, producing results in accordance with the prototype. This shows that the proposed methodology makes performing the mobility analysis of planar mechanisms, including complicated planar mechanisms, accurate, convenient, and fast.

Compared with the parallel mechanisms, the mobility analysis of the general multi-loop spatial mechanisms(GMSMs) is more difficult to obtain correct results. The reason is that its multi-loop is formed through several times of closings and there also exists motion coupling even strong coupling, where the over-constraints are concealed. However, the mobility analysis for this kind of mechanisms has been paid few attentions. A new systemic methodology for analyzing mobility is proposed for GMSMs also based on the screw theory. The key issue for mobility analysis is to recognize the over-constraint. Firstly, three theorems are given and point out: the reason and site of over-constraint occurrence, calculating the number of over-constraints by the screw theory, and how to analyze the over-constraints for a single-loop mechanism as well. Then, three closing forms for GMSMs are proposed including rigid closure, movable closure and dynamic closure, and for the three different forms the different analysis methods are also given. Especially, for the most difficult issue of GMSMs with the multi-loop closure in many times and the inevitable motion coupling, two important methods are proposed: “recognizing over-constraints by analyzing relative movement” and “recognizing over-constraints by virtual loop”. The two methods are well used to solve the issue. Above-mentioned principles are not only systematic and effective but also unified. They provide a theoretical basis for the general multi-loop spatial mechanisms.

Order analysis for multi-Bennett linkages is a difficult topic in kinematics. Traditional methods fail to obtain the order of multi-Bennett linkages due to considering the special geometric distributions among joint axes. An order principle for multi-Bennett linkages is presented. For a summated multi-Bennett linkage, three procedures are included in the order principle. Firstly, a homogeneous screw equation is obtained by taking linear superposition operations and then the maximum order is determined according to linear dependency of all screws. Secondly, two theorems are employed to determine the maximum order, where the first is used to judge the linear independency of four-system screws and the second is fit for identifying the linear independency of five-system screws. Lastly, all possible cases in the order range are considered until the valid order is screened out. For a syncopated multi-Bennett linkage, an equivalent summated model is built and then the order analysis is the same as that of summated linkages. In order to verify the effectiveness of the presented order principle, the orders of summated 5R and 6R linkages as well as a syncopated 6R linkage are analyzed. The computed orders of the former two summated linkages are both 4 and the computed order of the last syncopated 6R linkage is 5. The results coincide with the prototype data. The advantage of the proposed principle is that it can get the correct order of a multi-Bennett linkage without solving the geometric conditions of joint axes and has wide application in variety of multi-Bennett linkages.

A generally applicable criterion for all mechanism mobility has been an active domain in mechanism theory lasting more than 150 years. It is stated that the Modified Grübler-Kutzbach criterion for mobility has been successfully used to solve the mobility of many more kinds of mechanisms, but never before has anyone proven the applicability and generality of the Modified Grübler-Kutzbach criterion in theory. In order to fill the gap, the applicability and generality of the Modified Grübler-Kutzbach Criterion of mechanism mobility is systematically demonstrated. Firstly, the mobility research background and the Modified Grübler-Kutzbach criterion are introduced. Secondly, some new definitions, such as half local freedom, non-common constraint space of a mechanism and common motion space of a mechanism, etc, are given to demonstrate the correctness and broad applicability of the Modified Grübler-Kutzbach criterion. Thirdly, the general applicability of the Modified Grübler-Kutzbach criterion is demonstrated based on screw theory. The mobilities of the classical DELASSUS mechanisms and a modern planar parallel mechanism, are determined through the Modified Grübler-Kutzbach criterion, which are as examples to show the practical application of the Modified Grübler-Kutzbach criterion.

Singular configuration seriously affects the performance of the Gough-Stewart parallel mechanism and has attracted many researchers’ attentions. However, most of existing topics often focus on the position-singularity of the mechanism for a constant-orientation, but few reports research the orientation-singularity for a given position. In order to investigate the orientation-singularity of the Gough-Stewart parallel mechanisms with two dissimilar semi-regular hexagonal platforms for a given position, after constructing the discrimination matrix of the singular configuration of the mechanism and computing the determinant of this matrix by using unit quaternion as the orientation parameters which can avoid the singularities in parameterization, a general symbolic expression representing the three-dimensional orientation-singularity locus for a given position is obtained and the three-dimensional view of the orientation-singularity locus is further described. The orientation-singularity-free void exists inside the orientation-singularity locus, but the shape of the orientation-singularity-free void is irregular and inconvenient for the design of the mechanism. The minimal inscribed sphere of the three-dimensional orientation-singularity locus namely the orientation-singularity-free ball is described. The radius of the ball orientation-capability is used as the measurement for the orientation-singularity-free void size. A new efficient algorithm is proposed for the computation of the orientation-capability. Finally, the influences of the geometry parameters and the different positions of the mechanism on the orientation-capability are discussed. A new method of the singularity analysis of the Gough-Stewart parallel mechanism is advanced based on the unit quaternion, and the research finds have important referential value for the configuration parameters optimization of this class of the parallel mechanisms with the goal of having the maximal singularity-free zone.

The creation of novel kinematic structures of mechanisms still represents a major challenge in the quest for developing new, innovative devices. In this setting, computer models that can automatically generate and visualize all possible independent structures in an intuitive manner prove to be valuable as a support in the creative process of the designer. This paper proposes an automatic approach for establishing the complete atlas database of 2-DOF kinematic chains and a systematic approach for the creative design of mechanisms based on such an atlas. First, the transformation of the kinematic structure into a graph-based representation is addressed. Then, an approach for the generation of all nonfractionated topological graphs of 2-DOF (degrees of freedom) kinematic chains using contracted graphs as well as a method for synthesizing all the fractionated topological graphs through the combination of corresponding 1-DOF kinematic chains are addressed. Based on these methods, the complete atlas database of 2-DOF kinematic chains up to 15 links is established in this paper for the first time. Using this complete database, a systematic approach for the creative design of mechanisms can be derived, as illustrated for the example of an 11-link 2-DOF rode tractor.

It is difficult to manufacture parallel manipulators (PMs) with multiple revolute joint axes intersecting at one point. These types include the 3DOF spherical parallel manipulators (SPMs), the 4DOF 3R1T and 2R2T PMs, the 5DOF 3R2T PMs, etc. PMs with this problem are hard to achieve the expected mobility. In this paper, a 3-RPS cubic PM is studied, which has three rotational freedoms and is without those intersecting axes. The motion property of this PM will not change when the manufacturing errors exist. In order to show its orientation capability, the orientation workspace of this PM is analyzed. More discussions about the differences between the traditional SPMs and this PM are proposed. The results show that compared with the traditional SPMs, this 3-RPS cubic PM can also achieve three rotational motions with an enough orientation capability for applications and it has the advantage of easy fabrication.