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Shape fabrication from developable parts is the basis for arts such as papercraft and needlework, as well as modern architecture and CAD in general, and it has inspired much research. We observe that the assembly of complex 3D shapes…

The connection between self-assembly and computation suggests that a shape can be considered the output of a self-assembly ``program,'' a set of tiles that fit together to create a shape. It seems plausible that the size of the smallest…

Manually authoring 3D shapes is difficult and time consuming; generative models of 3D shapes offer compelling alternatives. Procedural representations are one such possibility: they offer high-quality and editable results but are difficult…

Mechanical assemblies can exhibit complex relative motions, during which collisions between moving parts and their surroundings must be avoided. To define feasible design spaces for each part's shape, "maximal" collision-free pointsets can…

Self-assembly is a fundamental concept in biology and of significant interest to nanotechnology. Significant progress has been made in characterizing and controlling the properties of the resulting structures, both experimentally and…

Assembly planning is a fundamental problem in robotics and automation, which involves designing a sequence of motions to bring the separate constituent parts of a product into their final placement in the product. Assembly planning is…

We use conformal maps to study a free boundary problem for a two-fluid electromechanical system, where the interface between the fluids is determined by the combined effects of electrostatic forces, gravity and surface tension. The free…

An important problem in geometric reasoning is to find the configuration of a collection of geometric bodies so as to satisfy a set of given constraints. Recently, it has been suggested that this problem can be solved efficiently by…

The purpose of this work is twofold: to present mathematical expressions for the kinematics of an articulated mechanism and to perform numerical experiments with the implemented code. The system of rigid parts is made of two slender bars…

This paper develops a planner to find an optimal assembly sequence to assemble several objects. The input to the planner is the mesh models of the objects, the relative poses between the objects in the assembly, and the final pose of the…

Robotic performance emerges from the coupling of body and controller, yet it remains unclear when morphology-control co-design is necessary. We present a unified framework that embeds morphology and control parameters within a single neural…

A flat sheet programmed with a planar pattern of spontaneous shape change will morph into a curved surface. Such metric mechanics is seen in growing biological sheets, and may be engineered in actuating soft matter sheets such as…

This paper proposes an adaptive pin-array fixture. The key idea of this research is to use the shape-memorable mechanism of pin array to fix multiple different shaped parts with common pin configuration. The clamping area consists of a…

This paper focuses on geometric methods for generating rational motions used in the design of single-loop rational linkages, 1-degree-of-freedom mechanisms that can execute prescribed spatial tasks. Building on established rational motion…

Part assembly is a typical but challenging task in robotics, where robots assemble a set of individual parts into a complete shape. In this paper, we develop a robotic assembly simulation environment for furniture assembly. We formulate the…

Assembly hinges on reliably forming connections between parts; yet most robotic approaches plan assembly sequences and part poses while treating connectors as an afterthought. Connections represent the foundational physical constraints of…

Shape-programmed sheets morph from one surface into another upon activation by stimuli such as illumination, and have attracted much interest for their potential engineering applications, especially in soft robotics. Complex shape changes…

Designing a robot or structure that can fold itself into a target shape is a process that involves challenges originated from multiple sources. For example, the designer of rigid self-folding robots must consider foldability from geometric…

It is shown that a compound elastic structure, which displays a dynamic instability, may be designed as the union (or 'fusion') of two structures which are stable when separately analyzed. The compound elastic structure has two degrees of…

Individualized manufacturing is becoming an important approach as a means to fulfill increasingly diverse and specific consumer requirements and expectations. While there are various solutions to the implementation of the manufacturing…