Spherical 4R Linkages Research Articles

Synthesis of an 8S5R mechanism in four-point rigid body guidance problem using Maple

In this paper, an accurate and graphical based method for synthesis of a nine-bar 8S5R mechanisms as a possible solution for four-point spatial rigid body guidance is presented. In the problem we are looking for a mechanism locating a rigid body in four specified postures in a 3D workspace. The posture includes position and orientation of a body. The degree of freedom of the mechanism is one, so by just one rotational or translational driving member, the desired motion can be generated. The method is based on the synthesis and design of two linkages; a six-bar 8S linkage and a spherical four-link 4R linkage. Coupler of the former is the desired body which should be navigated on the four desired postures and a coupler point of the latter, provides suitable movement for the input link of the former. The two linkages are connected using a revolute joint. Therefore, they form a nine-bar 8S5R mechanism. Since the graphical construction cannot be implemented in 3D design procedures by the conventional drawings, the symbolic mathematical software Maple-V is used to visualize the 3D concepts of the problem as well as accomplishing the accurate geometrical computations in the modeling. For completeness and simplicity, through the whole of the paper the associated commands of Maple are described. The mechanism can be used in the wide variety of motion generation problem in three-dimensional workspaces.

An improved mobility analysis for spherical 4R linkages

Mobility analyses of mechanisms represent an important step in the design process due to the fact that undesired types of motion could be avoided or conditions for achieving a specific mobility can be considered as restrictions for the design. This paper presents an improved mobility analysis for spherical four-bar linkages. As a result of this analysis, a simple, powerful and efficient graphical means of determining the range of travel for the angular motion of all the mechanism’s links can be devised. These graphical means are named mobility graphs and they could be considered as workspace atlas of the mechanism. The application of mobility graphs in the design process is illustrated by examples. Also, new assembly conditions for the linkage are presented and they extend those previously reported.