Developing a general mobility method/formula is a hot topic lasting for more than 150 years in kinematics. It is necessary to apply any mobility method to puzzling overconstrained mechanisms for verification of its generality. Altmann linkages are such recognized puzzling mechanisms that their mobility analysis is of important significance. A necessary condition for judging a general mobility method is that the method can be fit for Altmann linkages. Firstly, this study classes Altmann linkages into 17 types in terms of the numbers and types of kinematic pairs, and then Altmann overconstrained linkages are further classified into 4 types. Secondly, the mobility of Altmann overconstrained linkages is systematically analyzed by the Modified Grübler-Kutzbach criterion based on screw theory, where passive freedoms are defined as limb passive freedoms and mechanism passive freedoms. In addition, the full-cycle mobility is judged, which overcomes the shortcoming of instantaneous property of screw theory. It is shown that Modified Grübler-Kutzbach criterion not only obtains the correct numerical mobility, but also gives the mobility character by resolving reciprocal screws for the constraint system. This study lays the foundation of verification for the generality of Modified Grübler-Kutzbach criterion. Besides, Altmann overconstrained linkages almost comprise all kinds of modern parallel mechanisms and some classical mechanisms, which provides an important reference for mechanism mobility calculation.
The existence of coupling makes the parallel mechanism possess some special advantages over the serial mechanism, while it is just the coupling that brings about the parallel mechanism some limitations, such as complex workspace, high nonlinear relationship between input and output, difficulties in static and dynamic analysis, and the development of control system, which restricts its application fields. The decoupled parallel mechanism is currently one of the research focuses of the mechanism fields, while the study on the different characteristics between the decoupled and coupled parallel mechanisms has not been reported. Therefore, this paper performs the systematic comparative analysis of the 3-RPUR and the 3-CPR parallel mechanisms. The features of the two mechanisms are described and their movement forms are analyzed with screw theory. The inverse and forward displacement solutions are solved and the Jacobian matrices are obtained. According to the Jacobian matrices and by using the theory of physical model of the solution space, the workspace, dexterity, velocity, payload capability, and stiffness of the mechanisms are analyzed with plotting the indices atlases. The research results prove that the effects of the coupling on the parallel mechanism are double-side, and then the adoption of the decoupled parallel mechanism should be determined by the requirements of the concrete application situation. The contents of this paper should be useful for the type synthesis and practical application of the parallel mechanism.
Since the traditional Grbler-Kutzbach criterion fails in many overconstrained mechanisms, developing a general mobility formula is a hot topic lasting for more than 150 years in mechanisms. GOGU systematically investigated various mobility methods, and pointed that the methods were not fit for two kinds of paradoxical overconstrained mechanisms. The mobility on the two kinds of mechanisms is regarded as "Gogu problem" . The Modified Grbler-Kutzbach criterion has solved the mobility of the second kind of mechanisms in "Gogu problem" , and has developed into a systematic mobility methodology. Myard 5R linkage is one of the single-loop mechanisms involved in "Gogu problem" , its joint axes are distributed in space with special geometric conditions, which increases the difficulty of mobility analysis. The study is to calculate the global mobility of the Myard 5R linkage using the mobility methodology. Firstly, the mobility methodology based on screw theory is briefly introduced. Secondly, some homogeneous transforms are performed according to the D-H parameters and the invariance of the linkage plane symmetry is revealed, which provides an idea to judge a plane-symmetric loop. The special geometric features of the axes distribution are discussed as well. Finally, the global mobility of the Myard 5R linkage is determined by the Modified Grbler-Kutzbach criterion. The results show that the methodology can be applied to more paradoxical mechanisms.
It is widely used for the rotational parallel mechanism in the field of spatial orientation. While owing to the existence of coupling, the forward kinematic solution and the control of the general rotational parallel mechanism are especially difficult. If decoupling can be realized, the kinematic analysis of the mechanism will be very simple. Presently, the research of the parallel mechanism is focused on the inverse solution and structure optimization, and there is a lack of rotation decoupled parallel mechanisms (DPMs). So this paper proposes a family of 2 degree of freedom (DOF) rotational DPMs based on the four-bar linkage mechanism, and performs a characteristic analysis. This family of DPMs is composed of a moving platform, a fixed base and three limbs. Taking U__RRU__SPU DPM as an example, the motion feature of this DPM is analyzed with the constraint screw method, and its mobility is calculated by using the Modified Kutzbach-Grübler criterion. The inverse and forward displacement problems of the proposed parallel mechanism are solved. The decoupled feature of the proposed parallel mechanism is validated by the deduction of the expression of the Jacobian matrix. Three kinds of singularity conditions of this DPM are discussed, and the atlases of the output parameter concerning different geometric parameters are plotted with the theory of the physical model of the solution space. The proposition and characteristic analysis of the novel rotational DPMs in this paper should be useful for further research and application of the parallel mechanisms.
