Parameter analysis for the design of statically balanced serial linkages using a stiffness matrix approach with Cartesian coordinates

A statically balanced system is in equilibrium in every pose. In classical balancing solutions for serial linkages, each DOF is balanced by an independent element. Disadvantages are increased mass and inertia for counter-mass, and auxiliary links for spring solutions. Recent literature presents a method for balancing serial linkages without auxiliary links; using multi-articular springs. This method obtains constraint equations from the stiffness matrix. Downsides are different coordinate systems for describing locations and states, and criteria constraining attachments to fixed lines In the present paper Cartesian coordinates are implemented in the stiffness matrix approach. Goal is comparing the use of this single coordinate system to using multiple, and obtaining increased insight in and providing a visualization of parameter relations. The Cartesian coordinates are implemented, providing a simple, intuitive method for designing statically balanced serial linkages allowing for recognition of the full design space. Obtained parameter relations are visualized in an example.