Consistent coupling of positions and rotations for embedding 1D Cosserat beams into 3D solid volumes

The present article proposes a mortar-type finite element formulation for consistently embedding curved, slender beams into 3D solid volumes. Following the fundamental kinematic assumption of undeformable cross-section s, the beams are identified as 1D Cosserat continua with pointwise six (translational and rotational) degrees of freedom describing the cross-section (centroid) position and orientation. A consistent 1D-3D coupling scheme for this problem type is proposed, requiring to enforce both positional and rotational constraints. Since Boltzmann continua exhibit no inherent rotational degrees of freedom, suitable definitions of orthonormal triads are investigated that are representative for the orientation of material directions within the 3D solid. While the rotation tensor defined by the polar decomposition of the deformation gradient appears as a natural choice and will even be demonstrated to represent these material directions in a $$L_2$$ L 2 -optimal manner, several alternative triad definitions are investigated. Such alternatives potentially allow for a more efficient numerical evaluation. Moreover, objective (i.e. frame-invariant) rotational coupling constraints between beam and solid orientations are formulated and enforced in a variationally consistent manner based on either a penalty potential or a Lagrange multiplier potential. Eventually, finite element discretization of the solid domain, the embedded beams, which are modeled on basis of the geometrically exact beam theory, and the Lagrange multiplier field associated with the coupling constraints results in an embedded mortar-type formulation for rotational and translational constraint enforcement denoted as full beam-to-solid volume coupling (BTS-FULL) scheme. Based on elementary numerical test cases, it is demonstrated that a consistent spatial convergence behavior can be achieved and potential locking effects can be avoided, if the proposed BTS-FULL scheme is combined with a suitable solid triad definition. Eventually, real-life engineering applications are considered to illustrate the importance of consistently coupling both translational and rotational degrees of freedom as well as the upscaling potential of the proposed formulation. This allows the investigation of complex mechanical systems such as fiber-reinforced composite materials, containing a large number of curved, slender fibers with arbitrary orientation embedded in a matrix material.

Computational design of nanoscale rotational mechanics in de novo protein assemblies

Natural nanomachines like the F1/F0-ATPase contain protein components that undergo rotation relative to each other. Designing such mechanically constrained nanoscale protein architectures with internal degrees of freedom is an outstanding challenge for computational protein design. Here we explore the de novo construction of protein rotary machinery from designed axle and ring components. Using cryoelectron microscopy, we find that axle-ring systems assemble as designed and populate diverse rotational states depending on symmetry match or mismatch and the designed interface energy landscape. These mechanical systems with internal rotational degrees of freedom are a step towards the systematic design of genetically encodable nanomachines.

Aerial Tele-Manipulation with Passive Tool via Parallel Position/Force Control

This paper addresses the problem of unilateral contact interaction by an under-actuated quadrotor UAV equipped with a passive tool in a bilateral teleoperation scheme. To solve the challenging control problem of force regulation in contact interaction while maintaining flight stability and keeping the contact, we use a parallel position/force control method, commensurate to the system dynamics and constraints in which using the compliant structure of the end-effector the rotational degrees of freedom are also utilized to attain a broader range of feasible forces. In a bilateral teleoperation framework, the proposed control method regulates the aerial manipulator position in free flight and the applied force in contact interaction. On the master side, the human operator is provided with force haptic feedback to enhance his/her situational awareness. The validity of the theory and efficacy of the solution are shown by experimental results. This control architecture, integrated with a suitable perception/localization pipeline, could be used to perform outdoor aerial teleoperation tasks in hazardous and/or remote sites of interest.

Effects of Prosthetic Socket Design on Residual Femur Motion Using Dynamic Stereo X-Ray - A Preliminary Analysis

Individuals with transfemoral amputation experience relative motion between their residual limb and prosthetic socket, which can cause inefficient dynamic load transmission and secondary comorbidities that limit mobility. Accurately measuring the relative position and orientation of the residual limb relative to the prosthetic socket during dynamic activities can provide great insight into the complex mechanics of the socket/limb interface. Five participants with transfemoral amputation were recruited for this study. All participants had a well-fitting, ischial containment socket and were also fit with a compression/release stabilization socket. Participants underwent an 8-wk, randomized crossover trial to compare differences between socket types. Dynamic stereo x-ray was used to quantify three-dimensional residual bone kinematics relative to the prosthetic socket during treadmill walking at self-selected speed. Comfort, satisfaction, and utility were also assessed. There were no significant differences in relative femur kinematics between socket types in the three rotational degrees of freedom, as well as anterior-posterior and medial-lateral translation (p > 0.05). The ischial containment socket demonstrated significantly less proximal-distal translation (pistoning) of the femur compared to the compression/release stabilization socket during the gait cycle (p < 0.05), suggesting that the compression/release stabilization socket provided less control of the residual femur during distal translation. No significant differences in comfort and utility were found between socket types (p > 0.05). The quantitative, dynamic analytical tools used in the study were sensitive to distinguish differences in three-dimensional residual femur motion between two socket types, which can serve as a platform for future comparative effectiveness studies of socket technology.

Multi-point substructure coupling method to compensate multi-accelerometer masses in measuring rotation-related FRFs

Tool-tip Frequency Response Functions (FRFs) are often required in milling vibration analysis. Receptance coupling substructures analysis (RCSA) affords an efficient analytical way for different tool-tip FRFs prediction with only one modal test. The coupling theory includes both translational and rotational degrees of freedom, so rotation-related FRFs are essential to know in the test. The finite-differential technique is generally used to measure these special FRFs due to the avoidance of specialist equipment. The technique uses several translational accelerometers spatially placed close to each other to approximate the rotational vibration. However, the added sensor masses lead to the frequency shift of the test structure, and the phenomenon would aggravate as the sensors increase. The polluted measurement data would subsequently decrease the tool-tip FRFs prediction accuracy. Addressing this problem, this paper introduces a multi-point substructure coupling method to simultaneously compensate the multi-accelerometer masses in a single experimental setup. The proposed method considers the installed accelerators as multiple point masses and then uses inverse coupling calculation to isolate their effect. The compensation procedure is first effectively validated in simulation and experiment, and then it is integrated into an RCSA-based application of predicting different tool-tip dynamics. Experimental results show that the compensated FRF data can improve prediction accuracy, especially when predicting tools shorter than the tested tool.