Computational Kinematics is a wide field of science addressing applications ranging from robotics to mechanics, computer science, mathematics and computer graphics.

This paper presents a simple and highly visual approach for the type synthesis of a family of overconstrained parallel mechanisms that have one translational and two rotational movement capabilities. It considers, especially, mechanisms offering the accuracy and dynamic response needed for machining applications. This family features a spatial limb plus a member of a class of planar symmetrical linkages, the latter connected by a revolute joint either to the machine frame at its base link or to the platform at its output link. Criteria for selecting suitable structures from among numerous candidates are proposed by considering the realistic practical requirements for reconfigurability, movement capability, rational component design and so on. It concludes that a few can simultaneously fulfil the proposed criteria, even though a variety of structures have been presented in the literature. Exploitation of the proposed structures and evaluation criteria then leads to a novel five degrees of freedom hybrid module named TriMule. A significant potential advantage of the TriMule over the Tricept arises because all the joints connecting the base link and the machine frame can be integrated into one single, compact part, leading to a lightweight, cost effective and flexible design particularly suitable for configuring various robotized manufacturing cells.

We present singularity-free workspace optimization of a class of two-degree-of-freedom (2-DoF) parallel wrists with large rotation range capability. The wrists in consideration are kinematically equivalent to two families of 2-DoF homokinetic couplings. The first family comprises fully parallel wrists with N (N ≥ 3) double-universal ($\mathcal{UU}$) legs. The second family comprises spherical N-$\mathcal{UU}$ parallel wrists with interconnecting revolute ($\mathcal{R}$) joints. Both families belong to the more general class of zero-torsion parallel manipulators, and are, therefore, collectively referred to as zero-torsion wrists (ZTWs). We carry out a unified singularity-free workspace optimization by utilizing geometric properties of zero-torsion motion manifolds. Our work may serve as a conceptual guide to the design of ZTWs for large tilt-angle applications.

Higher-order derivatives of kinematic mappings give insight into the motion characteristics of complex mechanisms. Screw theory and its associated Lie group theory have been used to find these derivatives of loop closure equations up to an arbitrary order. In this paper, this is extended to the higher-order derivatives of the solution to these loop closure equations to provide an approximation of the finite motion of serial and parallel mechanisms. This recursive algorithm, consisting solely of matrix operations, relies on a simplified representation of the higher-order derivatives of open chains. The method is applied to a serial, a multi-DOF parallel, and an overconstrained mechanism. In all cases, adequate approximation is obtained over a large portion of the workspace.

Serial spherical linkages have been used in the design of a number of robots for minimally invasive surgery, in order to mechanically constrain the surgical instrument with respect to the incision. However, the typical serial spherical mechanism suffers from conflicting design objectives, resulting in an unsuitable compromise between avoiding collision with the patient and producing good kinematic and workspace characteristics. In this paper, we propose a multi-robot system composed of two redundant serial spherical linkages to achieve this purpose. A multi-objective optimization for achieving the aforementioned design goals is presented first for a single redundant robot and then for a multi-robot system. The problem of mounting multiple robots on the operating table as well as the way cooperative actions can be performed is addressed. The sensitivity of each optimal solution (single-robot and multi-robot) to uncertainties in the design parameters is investigated.

Tensegrity mechanisms are composed of rigid and tensile parts that are in equilibrium. They are interesting alternative designs for some applications, such as modeling musculo-skeleton systems. Tensegrity mechanisms are more difficult to analyze than classical mechanisms as the static equilibrium conditions that must be satisfied generally result in complex equations. A class of planar one-degree-of-freedom tensegrity mechanisms with three linear springs is analyzed in detail for the sake of systematic solution classifications. The kinetostatic equations are derived and solved under several loading and geometric conditions. It is shown that these mechanisms exhibit up to six equilibrium configurations, of which one or two are stable, depending on the geometric and loading conditions. Discriminant varieties and cylindrical algebraic decomposition combined with Groebner base elimination are used to classify solutions as a function of the geometric, loading, and actuator input parameters.

In this paper, a parametric analysis of the inverse dynamics of an upright partially unloaded walking is performed. This motion is produced through a gait-training machine emulating the over-ground walking using a body weight support mechanism and a cable-driven robot. The input motion is the kinematics of a normal gait, and the ultimate output result is the required tensions to be generated by the cable robot in order to drive the lower limb. The dynamic analysis is carried out based on the Newton–Euler approach. A Matlab Simscape model is also built to validate the analytical results. The obtained dynamic model is used to investigate the effect of the variation of the gait simulation parameters on the actuation wrench and the cable tensions. The obtained results could be used to determine the optimal design of the gait trainer actuators and they are useful in estimating optimal gait training parameters.

This paper deals with the kinematic analysis and enumeration of singularities of the six degree-of-freedom 3-RPS-3-SPR series–parallel manipulator (S–PM). The characteristic tetrahedron of the S–PM is established, whose degeneracy is bijectively mapped to the serial singularities of the S–PM. Study parametrization is used to determine six independent parameters that characterize the S–PM and the direct kinematics problem is solved by mapping the transformation matrix between the base and the end-effector to a point in ℙ7. The inverse kinematics problem of the 3-RPS-3-SPR S–PM amounts to find the location of three points on three lines. This problem leads to a minimal octic univariate polynomial with four quadratic factors.

This paper introduces a novel kinematic of a four degrees of freedom (DoFs) device based on Delta architecture. This new device is expected to be used as a haptic device for tele-operation applications. The challenging task was to obtain orientation DoFs from the Delta structure. A fourth leg is added to the Delta structure to convert translations into rotations and to provide translation of the handle. The fourth leg is linked to the base and to the moving platform by two universal joints. The architecture as well as the kinematic model of the new structure, called 4haptic, are presented. Comparisons in terms of kinematic behavior between the 4haptic device and the existing device developed based on spherical parallel manipulator architecture are presented. The results prove the improved behavior of the 4haptic device offering a singularity-free useful workspace, which makes it a suitable candidate to tele-operated system for Minimally Invasive Surgery. The dimensions of the 4haptic device, having the smallest workspace containing a prespecified region in space, are identified based on an optimal dimensional synthesis method.