Design and Synthesis of the Gravity Compensator with a Non-zero Length Spring

—It is well known that conventional linear spring directly jointed with a rotating link cannot ensure a complete gravity balancing. In this case, the application of zero length springs is suggested. The zero length spring corresponds to a spring with special coils ensuring zero elastic force for zero length of the spring. This type of spring is often used in theoretical solutions or in academic studies but rarely in real robotic structures. The use of traditional linear springs leads to inclusion of the auxiliary mechanism. The associated mechanisms are different and each of them requires its study and improvement. The applied methods for their study are various. They depend on the structure of the auxiliary mechanism and locations of balancing forces. This paper deals with design and synthesis of the gravity compensator including an auxiliary two-link dyad added to the rotating link. The balancing spring is installed vertically at the base. The choice of a vertical installation is due not only to constructive practicality but also to the fact that the mass of the spring system does not affect the balancing conditions of the rotating link. The aim of the study is to propose an analytically tractable solution permitting to synthesize such link lengths of the additional dyad that will provide a more optimal generation of the balancing moment. The efficiency of the suggested mechanism design is illustrated via numerical simulations. It is shown that by using a non-zero length spring a quasi-perfect balancing has been achieved.