Research on a new method for the degree of freedom analysis of parallel mechanism

Abstract

At present, traditional analysis methods sometimes show incompatibility when analyzing the degree of freedom (DOF) of parallel mechanisms. In this research, a new DOF analysis method (MV-DOF method) based on primary-ancillary motion theory is developed. The 4PPRRR series-parallel mechanism is taken as an example, the analysis results by using the MV-DOF method are compared with those of traditional inverse helix theory and modified Grübler-Kutzbach formula, respectively. The comparison shows that this MV-DOF method can always analyze the DOF of the 4PPRRR series-parallel mechanism accurately, while the other two traditional methods show inapplicability sometimes. During the analysis, an important rule is also found that the ancillary motion is equivalent to local constraint helix motion, but it is not always true in turn. Based on this MV-DOF method, a DOF cutting analysis way is also suggested. Any output point on a complex mechanism can be taken as a cutting point, along which the mechanism can be cut into two independent sub-mechanisms. The output DOF of each sub-mechanism can be analyzed separately by using the MV-DOF method, then the intersection can be obtained as the DOF of the whole mechanism at this output point. This research provides a new and effective analytical way for DOF analysis of parallel mechanisms.