Screw theory is a powerful mathematical tool for the kinematic analysis of mechanisms and has become a cornerstone of modern kinematics. Although screw theory has rooted itself as a core concept, there is a lack of generic software tools for visualization of the geometric pattern of the screw elements. This paper presents STORM, an educational and research oriented framework for analysis and visualization of reciprocal screw systems for a class of robot manipulator and mechanisms. This platform has been developed as a way to bridge the gap between theory and practice of application of screw theory in the constraint and motion analysis for robot mechanisms. STORM utilizes an abstracted software architecture that enables the user to study different structures of robot manipulators. The example case studies demonstrate the potential to perform analysis on mechanisms, visualize the screw entities and conveniently add new models and analyses.

The analysis of singularities is central to the development and control of a manipulator. However, existing methods for singularity set computation still concentrate on specific classes of manipulators. The absence of general methods able to perform such computation on a large class of manipulators is problematic because it hinders the analysis of unconventional manipulators and the development of new robot topologies. The purpose of this paper is to provide such a method for nonredundant mechanisms with algebraic lower pairs and designated input and output speeds. We formulate systems of equations that describe the whole singularity set and each one of the singularity types independently, and show how to compute the configurations in each type using a numerical technique based on linear relaxations. The method can be used to analyze manipulators with arbitrary geometry, and it isolates the singularities with the desired accuracy. We illustrate the formulation of the conditions and their numerical solution with examples, and use 3-D projections to visualize the complex partitions of the configuration space induced by the singularities.

This paper provides a method to compute all types of singularities of non-redundant manipulators with non-helical lower pairs and designated instantaneous input and output speeds. A system of equations describing each singularity type is given. Using a numerical method based on linear relaxations, the configurations in each type are computed independently. The method is general and complete: it can be applied to manipulators with arbitrary geometry; and will isolate singularities with the desired accuracy. As an example, the entire singularity set and its complete classification are computed for a two-degree-of-freedom mechanism. The complex partition of the configuration space by various singularities is illustrated by three-dimensional projections.

The paper discusses forward and inverse kinematics of a class of four-degree-of-freedom (DOF), four-legged parallel mechanisms providing three rotational and one translational DOFs. A fully parametric analytical form solution to the inverse-position problem is provided. All working modes of the mechanism are shown and discussed. The equations of the forward-position problem are obtained under different leg arrangements, and a numerical example is provided. New special geometries in the class are proposed, including one suitable for keyhole surgery.

The concept of constraint singularity is introduced. This is a phenomenon occurring in parallel mechanisms with reduced freedoms when the screw system, formed by the constraint wrenches in all legs, loses rank.