This paper provides a detailed review of the state of the art in product cost estimation covering various techniques and methodologies developed over the years. The overall work is categorized into qualitative and quantitative techniques. The qualitative techniques are further subdivided into intuitive and analogical techniques, and the quantitative ones into parametric and analytical techniques. Each of the techniques is then described and discussed, in detail, with further subdivisions. The paper also signifies the importance of cost estimation in the early phases of the design cycle and, as such, briefly discusses the current trends and future directions in the area. Research work carried out in the field with reference to specific applications is also reviewed. The paper provides a comprehensive literature review in the field and should be useful to researchers and practitioners interested in this field.

This paper looks at a class of mechanisms that change structure when erected or folded. The class includes a variety of artefacts and decorative gifts and boxes comprised of flat card creased to enable the folding or unfolding of a structure. Such a structure admits kinematic study in keeping with theory of mechanisms when the creases are treated as hinges joining card and paper panels treated as links. New horizons have been brought up in the use and mechanised manufacture of mechanisms of this kind. Here typical types are described in terms of their fundamental parts and their equivalent mechanisms. Screw system theory is brought into the analysis of mechanisms of these kinds, particularly those containing multiple loops. Different geometry and system combinations are used for the study of mobility and kinematics making use of the result from the equivalent screw systems.

The Kutzbach–Grübler mobility criterion calculates the degrees of freedom of a general mechanism. However, the criterion can break down for mechanisms with special geometries, and in particular, the class of so-called overconstrained parallel mechanisms. The problem is that the criterion treats all constraints as active, even redundant constraints, which do not affect the mechanism degrees of freedom. In this paper we reveal a number of screw systems of a parallel mechanism, explore their inter-relationship and develop an original theoretical framework to relate these screw systems to motion and constraints of a parallel mechanism to identify the platform constraints, mechanism constraints and redundant constraints. The screw system characteristics and relationships are investigated for physical properties and a new approach to mobility analysis is proposed based on decompositions of motion and constraint screw systems. New versions of the mobility criterion are thus presented to eliminate the redundant constraints and accurately predict the platform degrees of freedom. Several examples of overconstrained mechanisms from the literature illustrate the results.

Several models in NCG with mild changes to the standard model(SM) are introduced to discuss the neutrino mass problem. We use two constraints, Poincaré duality and gauge anomaly free, to discuss the possibility of containing right-handed neutrinos in them. Our work shows that no model in this paper, with each generation containing a right-handed neutrino, can satisfy these two constraints in the same time. So, to consist with neutrino oscillation experiment results, maybe fundamental changes to the present version of NCG are usually needed to include Dirac massive neutrinos.

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This paper reviews the Euler-Rodrigues formula in the axis-angle representation of rotations, studies its variations and derivations in different mathematical forms as vectors, quaternions and Lie groups and investigates their intrinsic connections. The Euler-Rodrigues formula in the Taylor series expansion is presented and its use as an exponential map of Lie algebras is discussed particularly with a non-normalized vector. The connection between Euler-Rodrigues parameters and the Euler-Rodrigues formula is then demonstrated through quaternion conjugation and the equivalence between quaternion conjugation and an adjoint action of the Lie group is subsequently presented. The paper provides a rich reference for the Euler-Rodrigues formula, the variations and their connections and for their use in rigid body kinematics, dynamics and computer graphics.

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This work provides a detailed survey of the kinematic design of MIS robots, addresses the research opportunity in MIS robots for kinematicians, and clarifies the kinematic point of view to MIS robots as a reference for the medical community.