'What the Tortoise said to Achilles': Lewis Carroll's Paradox of Inference

Lewis Carroll’s 1895 paper, 'What the Tortoise Said to Achilles' is widely regarded as a classic text in the philosophy of logic. This special issue of 'The Carrollian' publishes five newly commissioned articles by experts in the field. The original paper is reproduced, together with contemporary correspondence relating to the paper and an extensive bibliography

Explicit modeling of composite plates and beams in the dynamics of multibody systems

The state of the art dynamic response analysis of flexible multibody systems is currently restricted to elastic bodies with homogeneous materials. The requirements for high speed operation has made it necessary to use lightweight multi layered composite bodies in robotic systems and space structure applications. Dynamic modeling and analysis of such systems are particularly important since the effects of body flexibility to the performance are likely to be more pronounced. The eight-noded isoperimetric quadrilateral element with independent rotational and displacement degrees of freedom is extended to laminated composite elements. The element includes an arbitrary number of bonded layers, each of which may have a different thickness. The transverse shear deformation which is a predominant factor in the analysis of laminated composite structures is taken into account in developing the stiffness and mass matrices. The corresponding 3-D mode shapes are then incorporated to the multibody system dynamical equations. Floating body reference frames allow the selection of different boundary conditions, and the dynamical equations contain all the nonlinear interactions between the rigid and elastic motion. Example simulations are presented to illustrate the methods proposed

Challenges in modeling total knee arthroplasty and total hip replacement

AbstractTotal knee arthroplasty and hip replacement are commonly used procedures in which an ailing knee or hip joint is replaced with a carefully engineered artificial joint. Multibody models of healthy knee and hip joints are used extensively to design artificial knee and joints. The quality of the replacement joint is thus intrinsically related to the quality of the multibody models. In this work, the quality of a kinematic knee model is assessed by comparing predicted knee kinematics to cadaveric knee kinematics under several patellar overstuffing conditions. In addition, the micro motion at the hip joint (between the femoral head and the acetabulum) under varying loads is experimentally measured using a cemented and a cementless cadaveric hip joint

Challenges in modeling total knee arthroplasty and total hip replacement

AbstractTotal knee arthroplasty and hip replacement are commonly used procedures in which an ailing knee or hip joint is replaced with a carefully engineered artificial joint. Multibody models of healthy knee and hip joints are used extensively to design artificial knee and joints. The quality of the replacement joint is thus intrinsically related to the quality of the multibody models. In this work, the quality of a kinematic knee model is assessed by comparing predicted knee kinematics to cadaveric knee kinematics under several patellar overstuffing conditions. In addition, the micro motion at the hip joint (between the femoral head and the acetabulum) under varying loads is experimentally measured using a cemented and a cementless cadaveric hip joint

Computational strategies in the dynamic simulation of constrained flexible MBS

This research focuses on the computational dynamics of flexible constrained multibody systems. At first a recursive mapping formulation of the kinematical expressions in a minimum dimension as well as the matrix representation of the equations of motion are presented. The method employs Kane's equation, FEM, and concepts of continuum mechanics. The generalized active forces are extended to include the effects of high temperature conditions, such as creep, thermal stress, and elastic-plastic deformation. The time variant constraint relations for rolling/contact conditions between two flexible bodies are also studied. The constraints for validation of MBS simulation of gear meshing contact using a modified Timoshenko beam theory are also presented. The last part deals with minimization of vibration/deformation of the elastic beam in multibody systems making use of time variant boundary conditions. The above methodologies and computational procedures developed are being implemented in a program called DYAMUS

Optimum control forces for multibody systems with intermittent motion

The objective is to address the continuity of motion when a dynamical system is suddenly subjected to constraint conditions. Motion discontinuity due to the initial constraint violation is avoided by prior control forces that adjust the motion and yield velocity and acceleration consistent at the point of application of the constraint. The optimum control forces are determined for a specified control interval. The method proposed provides an optimum adjustment of the system's motion and assures that the stresses developed at the system components are kept within acceptable limits. The procedures developed will be illustrated making use of inequality constraints applied to obstacle avoidance problems in robotics

Hugh MacColl and Lewis Carroll: Crosscurrents in geometry and logic

Dans une lettre adressée à Bertrand Russell, le 17 mai 1905, Hugh MacColl raconte avoir abandonné l’étude de la logique après 1884, pendant près de treize ans, et explique que ce fut la lecture de l’ouvrage de Lewis Carroll, Symbolic Logic (1896), qui ralluma le vieux feu qu’il croyait éteint. Dès lors, il publie de nombreux articles contenant certaines de ses innovations majeures en logique. L’objet de cet article est de discuter la familiarité de MacColl et son appréciation du travail de Carroll, et de comprendre comment cela l’amena à réinvestir le domaine de la logique. Rien n’indique que les deux hommes se soient jamais rencontrés ou aient échangé une correspondance personnelle. Cependant, MacColl recensa dans le journal The Athenaeum plusieurs ouvrages de Carroll, essentiellement en géométrie et en logique. Souvent, Carroll répondait aux critiques de MacColl dans les éditions suivantes de ses ouvrages. Une discussion de ces sources fournit des éclaircissements intéressants sur les investigations mathématiques et logiques de MacColl et Carroll.In a letter to Bertrand Russell, dated 17 May 1905, Hugh MacColl tells how he abandoned the study of logic after 1884 for about thirteen years and how it was the reading of Lewis Carroll’s Symbolic Logic (1896) that ”rekindled the old fire which [he] thought extinct.” From then onwards, he published several papers containing some of his major logical innovations. The aim of this paper is to discuss MacColl’s acquaintance with and appreciation of Carroll’s work, and how that reading convinced him to come back into the realm of logic. There is no evidence that the two men ever met or exchanged any personal correspondence. However, MacColl reviewed in The Athenaeum several of Carroll’s books, mainly on geometry and logic. Often, Carroll replied to MacColl’s criticisms in the following editions of his works. A discussion of these sources provides interesting insights to MacColl’s (and Carroll’s) mathematical and logical investigations

Primary cup stability in THA with augmentation of acetabular defect. A comparison of healthy and osteoporotic bone

AbstractBackground contextReconstruction of acetabular defect has been advocated as standard procedure in total hip arthroplasty. The presence of bony defects at the acetabulum is viewed as a cause of instability and acetabular wall augmentation is often used without proper consideration of surrounding bone density. The initial cup-bone stability is, however, a challenge and a number of studies supported by clinical follow-ups of patients suggested that if the structural graft needs supporting more than 50% of the acetabular component, a reconstruction cage device spanning ilium to ischium should be preferred to protect the graft and provide structural stability. This study aims to (1) investigate the relationship between cup motion and bone density and (2) quantify the re-distribution of stress at the defect site after augmentation.HyphotesisPaprosky type I or II, acetabular defects, when reconstructed with bone screws supported by bioabsorbable calcified triglyceride bone cement are significantly less effective for osteoporotic bone than healthy bone.Materials and methodsAcetabular wall defects were reconstructed on six cadaveric subjects with bioabsorbable calcified triglyceride bone cement using a re-bar technique. Data of the specimen with higher bone density was used to validate a Finite Element Model. Values of bone apparent density ranging from healthy to osteoporotic were simulated to evaluate (1) the cup motion, through both displacement and rotation, (2) and the von Mises stress distribution.ResultsDefect reconstruction with bone screws and bioabsorbable calcified triglyceride bone cement results in a re-distribution of stress at the defect site. For a reduction of 65% in bone density, the cup displacement was similar to a healthy bone for loads not exceeding 300N, as load progressed up to 1500N, the reconstructed defect showed increase of 99μm (128%) in displacement and of 0.08° in rotation angle.ConclusionsBased on the results, we suggest that an alternative solution to wall defect augmentation with bone screws supported by bioabsorbable calcified triglyceride bone cement, be used for osteoporotic bone.Level of evidenceLevel IV, experimental and cadaveric study

Biomechanical Comparison of Unilateral and Bilateral Pedicle Screw Fixation after Multilevel Lumbar Lateral Interbody Fusion

Study Design Human Cadaveric Biomechanical Study Objectives Lumbar Lateral Interbody Fusion (LLIF) utilizing a wide cage has been reported as having favorable biomechanical characteristics. We examine the biomechanical stability of unilateral pedicle screw and rod fixation after multilevel LLIF utilizing 26 mm wide cages compared to bilateral fixation. Methods Eight human cadaveric specimens of L1-L5 were included. Specimens were attached to a universal testing machine (MTS 30/G). Three-dimensional specimen range of motion (ROM) was recorded using an optical motion-tracking device. Specimens were tested in 3 conditions: 1) intact, 2) L1-L5 LLIF (4 levels) with unilateral rod, 3) L1-L5 LLIF with bilateral rods. Results From the intact condition, LLIF with unilateral rod decreased flexion-extension by 77%, lateral bending by 53%, and axial rotation by 26%. In LLIF with bilateral rods, flexion-extension decreased by 83%, lateral bending by 64%, and axial rotation by 34%. Comparing unilateral and bilateral fixation, LLIF with bilateral rods reduced ROM by a further 23% in flexion-extension, 25% in lateral bending, and 11% in axial rotation. The difference was statistically significant in flexion-extension and lateral bending (P < .005). Conclusions Considerable decreases in ROM were observed after multilevel (4-level) LLIF utilizing 26 mm cages supplemented with both unilateral and bilateral pedicle screws and rods. The addition of bilateral fixation provides a 10-25% additional decrease in ROM. These results can inform surgeons of the incremental biomechanical benefit when considering unilateral or bilateral posterior fixation after multilevel LLIF

Biomechanical Comparison of Multilevel Stand-Alone Lumbar Lateral Interbody Fusion With Posterior Pedicle Screws: An In Vitro Study

Objective Lumbar lateral interbody fusion (LLIF) allows placement of large interbody cages while preserving ligamentous structures important for stability. Multiple clinical and biomechanical studies have demonstrated the feasibility of stand-alone LLIF in single-level fusion. We sought to compare the stability of 4-level stand-alone LLIF utilizing wide (26 mm) cages with bilateral pedicle screw and rod fixation. Methods Eight human cadaveric specimens of L1–5 were included. Specimens were attached to a universal testing machine (MTS 30/G). Flexion, extension, and lateral bending were attained by applying a 200 N load at a rate of 2 mm/sec. Axial rotation of ±8° of the specimen was performed at 2°/sec. Three-dimensional specimen motion was recorded using an optical motion-tracking device. Specimens were tested in 4 conditions: (1) intact, (2) bilateral pedicle screws and rods, (3) 26-mm stand-alone LLIF, (4) 26-mm LLIF with bilateral pedicle screws and rods. Results Compared to the stand-alone LLIF, bilateral pedicle screws and rods had 47% less range of motion in flexion-extension (p < 0.001), 21% less in lateral bending (p < 0.05), and 20% less in axial rotation (p = 0.1). The addition of bilateral posterior instrumentation to the stand-alone LLIF resulted in decreases of all 3 planes of motion: 61% in flexion-extension (p < 0.001), 57% in lateral bending (p < 0.001), 22% in axial rotation (p = 0.002). Conclusion Despite the biomechanical advantages associated with the lateral approach and 26 mm wide cages, stand-alone LLIF for 4-level fusion is not equivalent to pedicle screws and rods