Multi‐Pose Interactive Linkage Design

We present an interactive tool compatible with existing software (Rhino/Grasshopper) to design ring structures with a paradoxic mobility, which are self‐collision‐free over the complete motion cycle. Our computational approach allows non‐expert users to create these invertible paradoxic loops with six rotational joints by providing several interactions that facilitate design exploration. In a first step, a rational cubic motion is shaped either by means of a four pose interpolation procedure or a motion evolution algorithm. By using the representation of spatial displacements in terms of dual‐quaternions, the associated motion polynomial of the resulting motion can be factored in several ways, each corresponding to a composition of three rotations. By combining two suitable factorizations, an arrangement of six rotary axes is achieved, which possesses a 1‐parametric mobility. In the next step, these axes are connected by links in a way that the resulting linkage is collision‐free over the complete motion cycle. Based on an algorithmic solution for this problem, collision‐free design spaces of the individual links are generated in a post‐processing step. The functionality of the developed design tool is demonstrated in the context of an architectural and artistic application studied in a master‐level studio course. Two results of the performed design experiments were fabricated by the use of computer‐controlled machines to achieve the necessary accuracy ensuring the mobility of the models.

Section: Introductionmentioning

confidence: 76%

“…In general, one can perform collision detection numerically when the linkage geometry is established, e.g. [NBA19]. Once a self‐collision‐free linkage is obtained, we are forced to increase again the complexity of the linkage due to some realization constraints.…”

Section: Linkage Designmentioning

confidence: 99%

Invertible Paradoxic Loop Structures for Transformable Design

Nawratil

Rist

et al. 2020

“…Assemblies with mechanical joints can form dynamic mechanisms for transferring motions [MYY∗10], e.g., a linkage‐based mechanical toy that converts an input motion from a crank or motor to generate intriguing motions [CTN∗13,TCG∗14]. Assemblies with mechanical joints can also form objects whose poses are manually adjustable [KLY∗14, UTZ16, NBA19]. By the frictional contacts at joints, these articulated models [BBJP12, CCA∗12] can be stable at desired poses.…”

Section: Related Workmentioning

confidence: 99%

Worst‐Case Rigidity Analysis and Optimization for Assemblies with Mechanical Joints

Liu

et al. 2022

Figure 1: Given the assembly structure of the 153-brick LEGO Technic ROLLING CHASSIS (a), our method quantifies the rigidity of the structure (b1) and finds the worst-case external load configuration (yellow arrows) that maximally deforms it (c). A larger rigidity value indicates a more rigid assembly and thus greater resistance to external forces. After we strengthen the initial model as per the recommendation given by our method, the reinforced model (b2) has its rigidity value tripled, and undergoes less deformation than the initial one under the same loads that twist the model. The physical experiments (c) also show results that align with the analysis of our method.

“…The focus of these hinged assemblies is to make use of their multiple forms, and hinges just provide a way to transform across these forms. This makes them distinct from mechanical assemblies with hinges such as linkages [NBA19, UTZ16], whose focus is to transfer motion and force by transforming the parts. Research efforts have been devoted to computational design of three classes of hinged reconfigurable assemblies: a special geometric dissection called hinged dissection, transformables that can shift across different shapes, and foldable assemblies for space saving.…”

Section: Reconfigurable Assembliesmentioning

confidence: 99%

State of the Art on Computational Design of Assemblies with Rigid Parts

Wang

Song

Pauly

2021

An assembly refers to a collection of parts joined together to achieve a specific form and/or functionality. Designing assemblies is a non-trivial task as a slight local modification on a part's geometry or its joining method could have a global impact on the structural and/or functional performance of the whole assembly. Assemblies can be classified as structures that transmit force to carry loads and mechanisms that transfer motion and force to perform mechanical work. In this state-of-the-art report, we focus on computational design of structures with rigid parts, which generally can be formulated as a geometric modeling and optimization problem. We broadly classify existing computational design approaches, mainly from the computer graphics community, according to high-level design objectives, including fabricability, structural stability, reconfigurability, and tileability. Computational analysis of various aspects of assemblies is an integral component in these design approaches. We review different classes of computational analysis and design methods, discuss their strengths and limitations, make connections among them, and propose possible directions for future research.