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.

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.

Metamorphic mechanisms form a class of mechanisms that has the facilities to change configuration from one kind to another with a resultant change in the number of effective links and mobility of movement. This paper develops formal matrix operations to describe the distinct topology of configurations found in a metamorphic mechanism and to complete transformation between them. A new way is hence introduced for modeling topological changes of metamorphic mechanisms in general. It introduces a new elimination E-elementary matrix together with a U-elementary matrix to form an EU-elementary matrix operation to produce the configuration transformation. The use of these matrix operations is demonstrated in both spherical and spatial metamorphic mechanisms, the mechanistic models taken from the industrial packaging operations of carton folding manipulation that stimulated this study.

Extending the method coined virtual-center-based (VCB) for synthesizing a group of deployable platonic mechanisms with radially reciprocating motion by implanting dual-plane-symmetric 8-bar linkages into the platonic polyhedron bases, this paper proposes for the first time a more general single-plane-symmetric 8-bar linkage and applies it together with the dual-plane-symmetric 8-bar linkage to the synthesis of a family of one-degree of freedom (DOF) highly overconstrained deployable polyhedral mechanisms (DPMs) with radially reciprocating motion. The two 8-bar linkages are compared, and geometry and kinematics of the single-plane-symmetric 8-bar linkage are investigated providing geometric constraints for synthesizing the DPMs. Based on synthesis of the regular DPMs, synthesis of semiregular and Johnson DPMs is implemented, which is illustrated by the synthesis and construction of a deployable rectangular prismatic mechanism and a truncated icosahedral (C60) mechanism. Geometric parameters and number synthesis of typical semiregular and Johnson DPMs based on the Archimedean polyhedrons, prisms and Johnson polyhedrons are presented. Further, movability of the mechanisms is evaluated using symmetry-extended rule, and mobility of the mechanisms is verified with screw-loop equation method; in addition, degree of overconstraint of the mechanisms is investigated by combining the Euler's formula for polyhedrons and the Grübler–Kutzbach formula for mobility analysis of linkages. Ultimately, singular configurations of the mechanisms are revealed and multifurcation of the DPMs is identified. The paper hence presents an intuitive and efficient approach for synthesizing PDMs that have great potential applications in the fields of architecture, manufacturing, robotics, space exploration, and molecule research.

This paper presents a novel design of extensible continuum robots in light of origami-inspired folding techniques. The design starts from a modularized crease pattern, which consists of two triangular bases and three waterbomb bases, and generates a folding process for creating an origami waterbomb parallel structure. This further progresses to generating a compliant module with the origami parallel structure and a helical compression spring. A novel extensible continuum robot with the integrated compliant parallel modules is then proposed to imitate not only the bending motion but also the contraction of continuum creatures in nature. Mapping the origami parallel structure to an equivalent kinematic model, the motion characteristics of the origami structure are explored in terms of kinematic principles. The analysis reveals the mixed rotational and translational motion of the origami parallel module and the virtual axes for yaw and pitch motions. Following kinematics of the proposed continuum robot and features of the integrated helical spring in each module, three actuation schemes and resultant typical working phases with a tendon-driven system are presented. The design and analysis are then followed by a prototype of the extensible continuum robot with six integrated compliant modules connected in serial. The functionality of the proposed continuum robot with the origami parallel structure as its skeleton and the helical springs as the compliant backbone is validated by experimental results.