On a Model of a Pneumatically Actuated Mechanical System

Abstract

A model of a general mechanical system, comprising a pneumatic system coupled to a linkage mechanism, is developed. The dynamic system behavior is studied using the digital computer as a design tool to determine the effect on the performance of changing design parameters. Within practical limitations, models of this kind have been used to achieve optimum design. Novel methods are used to treat the two major components of the system. The pneumatic system is modeled using an equivalent flow area which is a function of the time-dependent pressure ratio. Differential equations used to solve for the transient flow in the reservoir/piping/piston system are derived here. The mechanism driven by the pneumatic system consists of multiple series chains of four-bar linkages. The first- and second-order kinematic ratios required in the dynamics are computed from new explicit expressions derived here. Frictional losses, impact, and flexibility of the mechanism are included in the dynamic model. The nonlinearity of the differential equations arises from: (a) the kinematics, (b) drag forces depending on velocity squared, (c) magnetic forces depending on time squared, and (d) the strong nonlinearity of the time-dependent pneumatic system. The system of equations is solved numerically to obtain the record of pressure, temperature, and leakage in the pneumatic system and the travel of the mechanisms versus time. Good agreement is obtained between the theoretical solution and actual tests.