Disclosure of Static Indenfinablity of Kinematic Chains with Passive Connection

Abstract

The aim of the research is disclosure of the static indefinability of kinematics with passive connections which allow getting a full picture on the distribution of internal forces in details of the device. It is known that the qualified design of any products, including machinery, fully depends on the nature of the distribution of internal forces in details and their maximum values. Having a complete picture of such distribution, the designer is able to offer the most appropriate construction from the point of view of its efficiency.

In some mechanisms besides reactions in kinematic pairs owing to payload some additional efforts are emerged which can be caused by elastic deformation of parts resulting from the so-called passive connections. Usually passive connections are introduced in order to reinforce mechanism rigidity and redistribute general power flow on the sub streams: that, above all, leads to a significant workload reduction on the elements of kinematic pairs and mass of parts.

For the solution of this problem one should use "a force method" which implies:

1. Formation of static indefinable kinematics design model with rotary pairs (hinges), taking into account all the equal external active and inertial forces.

2. A model of the equivalent system is formed in which one of the end joints is to move straight forward in the direction of the reaction in the hinge to the longitudinal axis of the section.

3. A single state of the system is considered and formula by Vereshchagin is used and specific relocation of the conditional rolling hinge center is determined.

4. A diagram of longitudinal, cross forces and bending moments of the system is built when ‘single’ force influences conditional mobile hinge.

5. A model of set system load condition is constructed; and from static equilibrium condition the second constituent of conditional mobile hinge reaction is determined which leads to disclosure of static indefinability.

6. Deformation correctness checking of the calculations and constructions is carried out.