A Modular Method for Mechanical Error Analysis of Planar Linkages Composed of Class II Assur Group Kinematic Chains

This paper presents a modular method for the mechanical error analysis of complex planar linkages. The topology of the linkage under investigation is decomposed into several class II Assur group kinematic chains (AGKCs) combined in a given sequence. Therefore, the mechanical error of the whole linkage can be analyzed by investigating the error propagations of adopted AGKCs in successive order. Because class II AGKCs are first served as modules, the mechanical error equations of these AGKCs in terms of each error in link lengths and joint variables can be pre-formulated and embedded in form of subroutines in any programmable language. Once the AGKCs constituting the linkage topology is identified, the corresponding subroutines are introduced to compute the error propagations in the linkage. Therefore, the presented modular approach can facilitate the analysis by concentrating on the topology decomposition instead of the algebraic derivation. Numerical examples are provided to illustrate the advantage and flexibility of the modular approach.

Improvement on Planar Mechanism Composition Principle

By investigation of movement of the Assur groups in normal connecting condition, and by inspection of the kinematic pair concept, the conclusions were found that “The freedom of Assur group is zero” in the Planar Mechanism Composition Principle conflicts with the fact that Assur group can move, and the external kinematic pairs of Assur group are inconsistent with the kinematic pair concept. Proposals were put forward then that the motion characteristics of Assur group should be studied in normal connecting conditions, Grade I Linkage Group should be introduced, and the PPP Type Linkage Group existence as an example was provided. Some new views were put forward in discussion of Planar Mechanism Composition Principle. And then an example of mechanism analysis was given to show that the correct statement of the Mechanism Composition Principle is helpful to solve mechanism analysis problems.

Incorrect application of the epicycloid equation to the planetary mechanism of the cotton harvester

The content of the paper is based on the mathematical construction of the parametric equation of the epi- and hypocycloid curve described by a circle point. The purpose of the paper is to present the equations of epi- and hypocycloids in a parametric form in relation to the epi- and hypocyclic mechanism in a form convenient for calculation; to present the results of computational experiments on constructing phase trajectories of motion of a moving point of an epi- and hypocycloid. A detailed analysis of the analytical model of epi- and hypocycloids circumscribed by a point of a circle (on a moving circle) has been made. The equations of epi- and hypocycloids are presented in parametric form as applied to the epi- and hypocyclic mechanism in a form convenient for calculation. The results of studies on the construction of phase trajectories of a moving point of an epi- and hypocycloid with an analysis of the obtained curves are presented. The analytical model of epi- and hypocycloids is of practical importance, since it allows designing geared linkage mechanisms formed by attaching two-wire Assur group of various modifications to the planetary mechanism, as the primary mechanism.

Structural Analysis of Linkage Mechanisms of Hydraulic Manipulators

The structural schemes of hydraulic manipulators used in the roundwood handling operations are presented. The seventeen schemes of manipulators are considered. The characteristic technological processes are identified, the nominal motions of the attachment mounted on the manipulator are described and the structure of the manipulator used in each process is considered. The variety of structures of linkage mechanisms in manipulators is associated both with the accumulation of Assur groups and with the increase in the Assur group class. Mechanisms with the number of Assur groups up to 4 are used. Assur groups of 2nd and 3rd classes are mainly found in the mechanisms. Adding the degree of freedom to the manipulator is accompanied by emerging of an additional kinematic chain in the structure. The structures studied are divided into two groups: the first covers the structures in which the input links are attached to the column; the second consists of structures with internal inputs. Variants of additional classification features are proposed for structures with internal inputs. The known provisions of structural analysis as a whole allow the analysis to be performed if the internal input is separated out as an individual input link. Otherwise, it is necessary to correct the approaches to the structural analysis of mechanisms having internal input links.

The Design of Looped-Synchronous Mechanism With Duplicated Spatial Assur-Groups

The looped-synchronous mechanism (LSM) is a special one degree-of-freedom (DOF) closed chain of transmission with a large number of duplicated units that synchronizes the motion of many output links. This kind of mechanism can be found in many applications such as stator blade adjusting mechanisms for various aero-engines. The LSMs are composed of a large number of links and joints and must be designed by specific means. Spatial Assur-group, which is a concept extended from traditional Assur-group(in planar scope), and usually with a little number of parts and joints, is used in this work to design LSM. First, based on the formula of DOF of spatial Assur-group, all possible combinations are listed and two feasible combinations are chosen as the main body of each unit of LSM, combining with a prime mover to meet the requirement to be inexpandable and adjustable. Second, the condition for transmission ratio of the used Assur-group to be 1 is distilled for being synchronous and looped under the situation that all units of LSM have the same topology. To meet the condition, the needed dimensional conditions are researched and mathematical deduction is used to figure out the possibilities. Third, after confirming that it is impossible to meet the condition strictly, an optimization method in the environment of Simulink is used to approach the condition as close as possible. Finally, numerical and dynamic simulations are carried out to verify the effectiveness of the mentioned methods.

Generation of tooth profile for Roots rotor based on virtual linkage associated with Assur group

This article, for the first time, presents the generation of Roots rotor tooth profiles based on an Assur-group-associated virtual linkage method. Taking the original Roots rotor as an example, structure and geometry of the Roots rotor are introduced, and based on the principle of inversion, an equivalent virtual linkage is identified for generating dedendum tooth profile of the rotor. Using linkage decomposition associated with elemental Assur groups, algorithm for computing the tooth curve is constructed leading to the explicit expression of rotor profile and the corresponding numerical simulation, verifying the validity of the proposed approach. For demonstration purpose, the virtual linkage method is then extended to the generation of tooth profiles for the variants of Roots rotors with arc-cycloidal curves and arc-involute curves. Integrated with computer-aided design, computer-aided engineering and computer-aided manufacturing software platforms, as well as the three-dimensional printing technology, this article provides an efficient and intuitive approach for Roots rotor system design, analysis and development.

Solving the Kinematics of the Planar Mechanism Using Data Structures of Assur Groups

This paper presents a systematic solution of the kinematics of the planar mechanism from the aspect of Assur groups. When the planar mechanism is decomposed into Assur groups, the detailed calculating order of Assur groups is unknown. To solve this problem, first, the decomposed Assur groups are classified into three types according to their calculability, which lays the foundation for the establishment of the automatic solving algorithm for decomposed Assur groups. Second, the data structure for the Assur group is presented, which enables the automatic solving algorithm with the input and output parameters of each Assur group. All decomposed Assur groups are stored in the component stack, and all parameters of which are stored in the parameter stacks. The automatic algorithm will detect identification flags of each Assur group in the component stack and their corresponding parameters in the parameter stacks in order to decide which Assur group is calculable and which one can be solved afterward. The proposed systematic solution is able to generate an automatic solving order for all Assur groups in the planar mechanism and allows the adding, modifying, and removing of Assur groups at any time. Two planar mechanisms are given as examples to show the detailed process of the proposed systematic solution.