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In this paper we present the synthesis of novel reactionless spatial three-degrees-of-freedom (3-DoF) and 6-DoF mechanisms without any separate counter-rotation, using four-bar linkages. Based on the conditions of dynamic balancing of a single planar four-bar linkage developed elsewhere, the spatial problem is shown to be equivalent to ensuring that the inertia tensor of reactionless four-bar linkage(s), which is(are) attached on the moving link of a reactionless four-bar linkage, remains constant while moving. The reactionless conditions for planar four-bar linkages undergoing spatial motion are first given. Then, reactionless spatial 3-DoF mechanisms using four-bar linkages are synthesized. A numerical example of the reactionless spatial 3-DoF mechanism is given and, with the help of the dynamic simulation software ADAMS, it is shown that the mechanism is reactionless for arbitrary trajectories. Finally, this mechanism is used to synthesize reactionless 6-DoF parallel mechanisms.

This paper addresses the dynamic balancing of multi-degree-of-freedom (multi-DOF) parallel mechanisms with multiple legs using the dynamic equivalence between point masses and arbitrary moving platforms. In this technique, proposed elsewhere, the mass and inertia of the moving platform are dynamically replaced by point masses located at the points of attachment of the legs to the platform and the mechanisms are balanced by considering each of the legs independently. In this paper, two, three, and four point masses are respectively discussed for different cases. Finally, some physical interpretations are given.

This paper presents the synthesis of a novel reactionless spatial 3-DOF mechanism using four-bar linkages without any counter-rotation. Based on the conditions of static and dynamic balancing of a single planar four-bar linkage developed elsewhere, the spatial problem is shown to be equivalent to verifying if the inertia tensor of reactionless four-bar linkages can be kept constant when the planar mechanism(s) is(are) moving. The reactionless conditions for planar four-bar linkages in space are first given. Then, reactionless spatial 3-DOF mechanisms using four-bar linkages are synthesized. A numerical example of the reactionless spatial 3-DOF mechanisms is given and, with the help of the dynamic simulation software ADAMS, it is shown that the mechanisms are reactionless for any trajectory and can be used to synthesize 6-DOF reactionless mechanisms.

Singularity is a fundamental problem in the analysis of parallel mechanisms. The distribution of singularity in workspace will determine to a great extent the properties of parallel mechanisms. In this paper, we will study the distribution of actuator singularity, which can also be applied to analyze end-effector singularity. A very important observation has been made that these two kinds of singularities are caused by the parameterization of a configuration manifold by actuator coordinates or end-effector coordinates. Despite the various styles of singularities of parallel mechanisms, there are some rules which govern the behavior of stable singularities. These rules provide some useful ideas in the design of redundant parallel mechanisms so as to achieve better performance in high speed motion and improve their stiffness. Optimal kinematic and dynamic control algorithms are designed and implemented which make use of the redundancy of the parallel mechanism. Experimental results agree with our expectation.

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In this paper, the design and dynamic balancing of a novel 3-DOF parallel mechanism referred to as parallelepiped mechanism are addressed. Two types of actuation schemes of the mechanism are considered. The balancing equations are derived by imposing that the center of mass of the mechanism is fixed and that the total angular momentum is constant with respect to a fixed point. Optimization is performed to determine the counterweights and counter-rotations based on the balancing conditions. The dynamic simulation software ADAMS is used to simulate the motion of the 3-DOF parallelepiped mechanisms and to verify that the mechanisms are reactionless at all times and for any trajectory. A numerical example of a reactionless 3-DOF parallelepiped mechanism is given. It is shown that 3-DOF parallelepiped mechanisms can be completely balanced and used to synthesize 6-DOF reactionless manipulators. Additionally, the inverse and direct kinematic problems of the 3-DOF parallelepiped mechanisms as well as simulation tools for demonstrating the characteristics of the mechanisms are also introduced in this paper.