Precision-point synthesis problems for design of four-bar linkages have typically been formulated using two approaches. The exclusive use of path-points is known as “path synthesis,” whereas the use of poses, i.e., path-points with orientation, is called “rigid-body guidance” or the “Burmester problem.” We consider the family of “Alt–Burmester” synthesis problems, in which some combination of path-points and poses is specified, with the extreme cases corresponding to the classical problems. The Alt–Burmester problems that have, in general, a finite number of solutions include Burmester's original five-pose problem and also Alt's problem for nine path-points. The elimination of one path-point increases the dimension of the solution set by one, while the elimination of a pose increases it by two. Using techniques from numerical algebraic geometry, we tabulate the dimension and degree of all problems in this Alt–Burmester family, and provide more details concerning all the zero- and one-dimensional cases.

This paper presents a procedure to synthesize planar rigid-body mechanisms, containing both prismatic and revolute joints, capable of approximating a shape change defined by a set of morphing curves in different positions. The existing mechanization process is extended specifically to enable the design of morphing aircraft wings. A portion of the closed-curve morphing chain that has minimal displacement is identified as the structural ground after the segmentation process. Because of the revolute joints placed at the endpoints of the ground section, the moving links of the fixed-end morphing chain need to be repositioned relative to each of the desired wing shapes so as to minimize the error in approximating them. With the introduction of prismatic joints, a building-block approach is employed to mechanize the fixed-end morphing chain. The blocks are located in an assembly position to generate a single degree-of-freedom (DOF) mechanism. Because of the additional constraints associated with prismatic joints compared to revolute joints, the size of the solution space is reduced, so random searches of the design space to find solution mechanisms are ineffective. A multi-objective genetic algorithm is employed instead to find a group of viable designs that tradeoff minimizing matching error with maximizing mechanical advantage. The procedure is demonstrated with a synthesis example of a 1-DOF mechanism approximating eight closed-curve wing profiles.

This letter investigates the mathematical relationships between the positions and orientations at the segment tips of a piecewise constant curvature (PCC) continuum robot with up to three segments. For one-segment, a reachability criterion is proposed, simplifying the calculation of the neighboring orientation. For two-segments, a reachability criterion is proposed and the redundancy of its inverse kinematics solution is found, establishing a circle of tip locations. For three-segments, the redundancy of the inverse kinematics includes tips that lie on a sphere providing a closed-form solution to the inverse kinematics problem. These relationships are derived from the unique characteristics of the bisecting plane of a single segment. The degenerate cases for the solutions are also addressed. These outcomes stem from a specific PCC parametrization, with implications extending to the general PCC model. Note that this study is grounded solely in simulation.

The estimation of the centre of mass position in humans is usually based on biomechanical models developed from anthropometric tables. This method can potentially introduce errors in studies involving elderly people, since the ageing process is typically associated with a modification of the distribution of the body mass. In this paper, an alternative technique is proposed, and evaluated with an experimental study on 9 elderly volunteers. The technique is based on a virtual chain, identified from experimental data and locating the subject's centre of mass. Its configuration defines the location of the centre of mass, and is a function of the anatomical joint angles measured on the subject. This method is a valuable investigation tool in the field of geronto-technology, since it overcomes some of the problems encountered with other CoM estimation methods.

This paper proposes a method for modeling the center of mass (CoM) of humanoid robots. The method is based on the statically equivalent serial chain (SESC) model, a serial chain representation of any multi-link branched chain. An algorithm is presented to automatically construct the SESC of a symmetric anthropomorphic architecture. We also show the use of SESC modeling in the projection of the CoM when the kinematic chain is not positioned on a horizontal plane. Finally, after validating these developments on the HOAP-3 experimental humanoid robot platform, we discuss the interest of this modeling in other areas of research.