DOF Calculation Method of Planar Mechanisms Based on Constraint Normal Line

In the analysis and calculation of the degree of freedom (DOF) of mechanisms, it is generally a complicated problem to judge the virtual constraint correctly. Under what conditions do virtual constraints exist, and how many virtual constraints are there? Understanding these problems can contribute to effectively tackling the difficulty of calculating the DOF. With planar mechanisms as a research object, the constraints among various components are simplified into point constraints, and the common normal at a constraint point is referred to as normal. According to whether a constraint point can move relative to the frame in its normal direction, normals are divided into different categories. Based on the geometric theorem for judging the DOF of a workpiece, a set of geometric theorems for judging the DOF of components and their nature, over-constraint, and quantity are established. After the correlation between virtual constraints and over-constraints is clarified, the total number of virtual constraints in a mechanism is calculated. The analysis and calculation of the DOF of several typical planar mechanisms demonstrate that the new method is logically rigorous, simple, and intuitive, and the DOF of a mechanism can be accurately calculated.