As shown in this paper, when designing parallel manipulators for tasks involving less than six degrees of freedom, the topology can be laid out by resorting to qualitative reasoning. More specifically, the paper focuses on cases whereby the manipulation tasks pertain to displacements with the algebraic structure of a group. Besides the well-known planar and spherical displacements, this is the case of displacements involving: rotation about a given axis and translation in the direction of the same axis (cylindrical subgroup); translation in two and three dimensions (two- and three-dimensional translation subgroups); three independent translations and rotation about an axis of fixed direction, what is known as the Scho¨nflies subgroup; and similar to the Scho¨nflies subgroup, but with the rotation and the translation in the direction of the axis of rotation replaced by a screw displacement. For completeness, the fundamental concepts of motion representation and groups of displacements, as pertaining to rigid bodies, are first recalled. Finally, the concept of Π-joint, introduced elsewhere, is generalized to two and three degrees of freedom, thereby ending up with the Π2-and the Π3-joints, respectively.

The design of a robotic manipulator begins with the dimensioning of its various links to meet performance specifications. However, a methodology for the determination of the manipulator architecture, i.e., the fundamental geometry of the links, regardless of their shapes, is still lacking. Attempts have been made to apply the classical paradigms of linkage synthesis for motion generation, as in the Burmester Theory. The problem with this approach is that it relies on a specific task, described in the form of a discrete set of end-effector poses, which kills the very purpose of using robots, namely, their adaptability to a family of tasks. Another approach relies on the minimization of a condition number of the Jacobian matrix over the architectural parameters and the posture variables of the manipulator. This approach is not trouble-free either, for the matrices involved can have entries that bear different units, the matrix singular values thus being of disparate dimensions, which prevents the evaluation of any version of the condition number. As a means to cope with dimensional inhomogeneity, the concept of characteristic length was put forth. However, this concept has been slow in finding acceptance within the robotics community, probably because it lacks a direct geometric interpretation. In this paper the concept is revisited and put forward from a different point of view. In this vein, the concept of homogeneous space is introduced in order to relieve the designer from the concept of characteristic length. Within this space the link lengths are obtained as ratios, their optimum values as well as those of all angles involved being obtained by minimizing a condition number of the dimensionally homogeneous Jacobian. Further, a comparison between the condition number based on the two-norm and that based on the Frobenius norm is provided, where it is shown that the use of the Frobenius norm is more suitable for design purposes. Formulation of the inverse problem—obtaining link lengths—and the direct problem—obtaining the characteristic length of a given manipulator—are described. Finally a geometric interpretation of the characteristic length is provided. The application of the concept to the design and kinetostatic performance evaluation of serial robots is illustrated with examples.

Conventional soft pneumatic actuators (SPAs) are made of soft materials that facilitate safe interaction and adaptability. In positioning and loading tasks, however, SPAs demonstrate limited performance. In this article, we extend the current designs of SPAs upon integrating a tendon-driven parallel mechanism into a pneumatic origami chamber, inspired by the performances and structures of vertebrates. The inner rigid/outer soft actuator exploits the advantages of both, parallel mechanisms to achieve precise, versatile motion, and SPAs, to form a compliant, modular structure. With the antagonistic actuation of tendons-pulling and air-pushing, the actuator can exhibit multimode motion, tunable stiffness, and load-carrying maneuvers. Kinematic and quasi-static models are developed to predict the behavior and to control the actuator. Using readily accessible materials and fabrication methods, a prototype was built, on which validation experiments were conducted. The results prove the effectiveness of the model, and demonstrate the motion and stiffness characteristics of the actuator. The design strategy and comprehensive guidelines should expand the capabilities of soft robots for wider applications, and facilitate the development of robots with rigid-soft hybrid structures.

The concept of virtual power is first defined as the power measured, in a noninertial frame, in an epicyclic gear train. We then introduce the concept of virtual-power ratio, an invariant related to the power loss in an epicyclic system. It is shown that virtual-power flow and balance exist in an epicyclic gear train, based on which a novel algorithm to compute the gear-mesh powerloss and the train efficiency is formulated. This algorithm is general enough to be applied to any given epicyclic gear train. Our results are compared with previous work on the subject.