A New Universal Formula of Degree of Freedom for Planar Mechanism

Abstract

Without taking into account of redundant constraints,common constraints and isolated degree of freedom（DOF）,the traditional DOF calculation formulas are inefficient in calculating the DOF of planar mechanism in certain complicated cases.In addition,recalculating is needed when the configuration of mechanisms is changed.To solve these problems,a novel universal formula of DOF for planar mechanisms is presented based on the effectiveness impact of the components on the relation of input and output motion of mechanism.The algebraic relationship between redundant constraints,common constraints,partial DOF and the DOF of mechanism is studied respectively.The valid components,valid loops and higher pairs are defined as formula variables.The new formula does not need to calculate compound hinges and lower pairs and overcomes the invalidity of traditional formulas,which can be used directly for all kinds of planar mechanisms.In addition,by defining valid loops of mechanisms,the new formula emphasizes the impact of components,the basic unit of mechanisms,on the DOF of mechanism,which can avoid recalculating when the configuration of mechanisms is slightly changed.Contrast examples are presented to show the simplicity and validity of the new formula,which can be applied to ad-hoc planar mechanisms that couldn’t be solved by traditional formulas.

Keywords

• DOF calculation
• Planar mechanism
• Redundant constraint
• Common constraint
• Partial DOF