This short paper outlines how polynomial chaos theory (PCT) can be utilized for manipulator dynamic analysis and controller design in a 4-DOF selective compliance assembly robot-arm-type manipulator with variation in both the link masses and payload. It includes a simple linear control algorithm into the formulation to show the capability of the PCT framework.

Cable-driven robots and multifinger grasps are closely related to each other by the fact that both systems can provide unidirectional forces to the object to be constrained. While prior research primarily related cable-driven robots to grasps without friction, this article seeks to establish relationships between certain cable-driven robots and grasps with friction. Those relationships are used to transfer the antipodal grasp theorem to cable-driven robots, resulting in the so-called antipodal cable theorem. A planar and spatial version are presented.

Singular configurations where a parallel manipulator can lose stiffness are well documented and studied in literature. There exist many proposed measures on how close a pose is to these singularities. This paper develops a framework which unites many of the existing measures, provides further understanding for others, and creates new ones. The framework originates from a physical understanding of singularities with a natural progression to a constrained optimization problem. The solution to the optimization problem is a simple general eigenvalue problem of constant matrices. The power of this new framework is that it is easy to compare existing measures and develop new ones. Several examples of measures within the framework are given.

Although cable-driven robots and parallel manipulators have very similar architecture, the presence of the unidirectional constraints in cable-driven robots makes it impossible to apply many of the concepts and methods used for parallel manipulators. Instead many tools from grasping are more suitable, since fingers also provide unidirectional constraints. This article reviews some of the connections, provides some basic definitions that we hope leads to standardized terminology for cable-driven robots, and finally transfers the antipodal grasping theorem to planar cable-driven robots.

Singularities of parallel manipulators cause severe problems in the use of such manipulators. Likewise, finding how close the manipulator is to a singularity is key to its operation. This article outlines a new method to define "closeness" to singularities based on constrained optimization and its resulting general eigenvalue problem. This framework joins together many existing techniques into one unified theory. From this framework, the similarities and differences between measures can be easily identified, and new measures (e.g. natural frequency) can be derived.

At a singular configuration the end-effector of a parallel manipulator may become underconstrained, i.e. instantaneous motion may become possible. The unconstrained motion may be only instantaneous, or it can result in finite motion, also known as self-motion. This article presents two different approaches to analyze the potential for large motion at a singular configuration: (1) A necessary (but not sufficient) condition for self-motion is derived that assumes that the manipulator has perfect precision; (2) The unconstrained motion is analyzed based on finite clearance in the joints. Numerical results are presented and compared.