Dynamic balance eliminates the fluctuating reaction forces and moments induced by high-speed robots that would otherwise cause undesired base vibrations, noise and accuracy loss. Many balancing procedures, such as the addition of counter-rotating inertia wheels, increase the complexity and motor torques. There exist, however, a small set of closed-loop linkages that can be balanced by a specific design of the links' mass distribution, potentially leading to simpler and cost-effective solutions. Yet, the intricacy of the balance conditions hinder the extension of this set of linkages. Namely, these conditions contain complex closed-form kinematic models to express them in minimal coordinates. This paper presents an alternative approach by satisfying all higher-order derivatives of the balance conditions, thus avoiding finite closed-form kinematic models while providing a full solution for arbitrary linkages. The resulting dynamic balance conditions are linear in the inertia parameters such that a null space operation, either numeric or symbolic, yield the full design space. The concept of inertia transfer provides a graphical interpretation to retain intuition. A novel dynamically balanced 3-RSR spatially moving mechanism is presented together with known examples to illustrate the method.

Fast-moving industrial robots exert large varying reaction forces and moments on their base frame, inducing vibrations, wear and accuracy degeneration. These shaking forces and moments can be eliminated by a specific design of the mass distribution of the robot links, resulting in a dynamically balanced mechanism. Obtaining the conditions for dynamic balance proves to be a hurdle even for simple planar parallel mechanisms due to the required inclusion and inspection of the kinematic relations. In this paper, a screw theory based methodology is presented, which gives and solves the necessary instantaneous dynamic balance conditions for planar and spatial mechanisms in an uniform and geometrical manner. Instantaneous dynamic balance yields a pose in which robot accelerations induce no shaking forces and moments. This is interpreted as an intersection point of multiple reactionless paths. This method is applied to a 2-DOF planar mechanism, named the Fuga I, for which it resulted in two perpendicularly intersecting reactionless paths, intersecting in the middle of the workspace. Experiments on this demonstrator validated the instantaneous dynamic balance by showing a reduction of approximately 95% of the peak-to-peak shaking forces and moments over the intersecting reactionless paths.

Higher-order derivatives of kinematic mappings give insight into the motion characteristics of complex mechanisms. Screw theory and its associated Lie group theory have been used to find these derivatives of loop closure equations up to an arbitrary order. In this paper, this is extended to the higher-order derivatives of the solution to these loop closure equations to provide an approximation of the finite motion of serial and parallel mechanisms. This recursive algorithm, consisting solely of matrix operations, relies on a simplified representation of the higher-order derivatives of open chains. The method is applied to a serial, a multi-DOF parallel, and an overconstrained mechanism. In all cases, adequate approximation is obtained over a large portion of the workspace.