A method for improving dynamic characteristics of planar linkages by activelyvarying the speed function of the input link is presented. Design criteria and constraints for thedynamic design of variable speed planar linkages are developed. Both analytical and optimizationapproaches for determining suitable input speed functions to minimize the driving torque, theshaking moment, or both simultaneously of planar linkages, subject to various design requirementsand constraints, are derived. Finally, some examples are given to illustrate the design procedureand to verify its feasibility.
The dynamic balancing is an important issue in mechanism design. For the existing balancing methods, both passive and active ones, there is still room for improvement in adaplability and independency. In view of this, a concept of active balancer is developed as a new solution for the dynamic balancing with more flexibility. The proposed balancer is an independent additional device with a control system inside, which consists of a two-degree-of-freedom （DOF） linkage and a controllable motor, and can be attached to a machine expediently with little change to its original structure and motion. One of the two inputs of the two-DOF linkage shares the same shaft with its output, which is connected to the input shaft of a machine to be balanced and driven by the original actuator. The other input is driven by the control motor. By properly selecting the speed trajectories of the control motor and link parameters of the two-DOF linkage, one or more dynamic effects of the mechanisms can be minimized or eliminated adaptively. The design procedure of the active balancer is put forward and a two-step optimization is developed to find out optimal design parameters of the balancer for various design requirements and constraints. Taking a force-balanced crank-rocker mechanism as the reference mechanism, numerical examples are given to illustrate the design procedure. The balancing effects of the proposed balancer are compared with those of the existing adding dyads （DYAD） method. The results show that the introduction of the control system provides the active balancer with better balancing effect and more flexibility than the DYAD method. A considerable reduction in the dynamic effects （input torque, shaking moment and shaking force） can be achieved for different balancing object by designing the structural and control parameters of the balancer, and the deterioration of dynamic performance caused by alterative working conditions can be compensated effectively by redesigning the control parameters.
