Rigid-body Positions Research Articles

Biplanar Videoradiography to Study the Wrist and Distal Radioulnar Joints.

Accurate measurement of skeletal kinematics in vivo is essential for understanding normal joint function, the influence of pathology, disease progression, and the effects of treatments. Measurement systems that use skin surface markers to infer skeletal motion have provided important insight into normal and pathological kinematics, however, accurate arthrokinematics cannot be attained using these systems, especially during dynamic activities. In the past two decades, biplanar videoradiography (BVR) systems have enabled many researchers to directly study the skeletal kinematics of the joints during activities of daily living. To implement BVR systems for the distal upper extremity, videoradiographs of the distal radius and the hand are acquired from two calibrated X-ray sources while a subject performs a designated task. Three-dimensional (3D) rigid-body positions are computed from the videoradiographs via a best-fit registrations of 3D model projections ontoto each BVR view. The 3D models are density-based image volumes of the specific bone derived from independently acquired computed-tomography data. Utilizing graphics processor units and high-performance computing systems, this model-based tracking approach is shown to be fast and accurate in evaluating the wrist and distal radioulnar joint biomechanics. In this study, we first summarized the previous studies that have established the submillimeter and subdegree agreement of BVR with an in vitrooptical motion capture system in evaluating the wrist and distal radioulnar joint kinematics. Furthermore, we used BVR to compute the center of rotation behavior of the wrist joint, to evaluate the articulation pattern of the components of the implant upon one another, and to assess the dynamic change of ulnar variance during pronosupination of the forearm. In the future, carpal bones may be captured in greater detail with the addition of flat panel X-ray detectors, more X-ray sources (i.e., multiplanar videoradiography), or advanced computer vision algorithms.

Construction of low degree rational motions

Construction of rational spline motions is an important issue in robotics, animations and related fields. In this paper a geometric approach to interpolate given sequence of rigid body positions is considered, which, in contrast to standard approaches, is free of choosing parameter values in advance and it enables the lowest possible degree of the motion. A general solution to the problem how to interpolate 2n given positions by rational motion of degree 2n is presented and two particular cases, motions of degree six and eight, are studied in more detail. This interpolation scheme is further generalized to a method for constructing first order geometric continuous rational spline motions of degree six. Numerical examples are given which confirm the presented theoretical results.

On the dynamic simulation of eccentricity errors in planetary gears

Eccentricity errors are incorporated into a planetary gear lumped parameter model in which deflections, errors and gear geometry are coupled. In the presence of errors, rigid-body positions and motions are perturbed leading to initial separations between tooth flanks and inertial excitations caused by unsteady rotational speeds. The equations of motion are solved by combining a time-step scheme, a contact algorithm and a fixed-point method, which make it possible to determine and use mesh instantaneous characteristics in the calculations of tooth loads. A number of quasi-static and dynamic results are presented which show that eccentricities can be highly influential on planetary gear dynamic behaviour. Finally, the interest of floating members in equalizing planet dynamic loading is demonstrated and commented upon.

A Method of Type Map for Rigid-Body Guidance Based on Burmester Curve

The Burmester curve plays an important role in rigid-body guidance of four-bar linkage, but it still had serious blindness because two center points or circle points should be assigned arbitrary. So a method of Type Map for rigid-body guidance was proposed in this paper. All the four-bar linkages synthesized by burmester curve can be classified in accordance to their attributes. Using this method, satisfactory four-bar linkages can be obtained quickly for the given four rigid-body positions. An algorithm was proposed to define the discrimination of the Type Map in depth. Based on the platform of Matlab, a program was developed to realize the automatic design and visualize the guidance synthesis for four-bar linkage. The result proved the method to be feasible and effective.

SnugDock: Paratope Structural Optimization during Antibody-Antigen Docking Compensates for Errors in Antibody Homology Models

High resolution structures of antibody-antigen complexes are useful for analyzing the binding interface and to make rational choices for antibody engineering. When a crystallographic structure of a complex is unavailable, the structure must be predicted using computational tools. In this work, we illustrate a novel approach, named SnugDock, to predict high-resolution antibody-antigen complex structures by simultaneously structurally optimizing the antibody-antigen rigid-body positions, the relative orientation of the antibody light and heavy chains, and the conformations of the six complementarity determining region loops. This approach is especially useful when the crystal structure of the antibody is not available, requiring allowances for inaccuracies in an antibody homology model which would otherwise frustrate rigid-backbone docking predictions. Local docking using SnugDock with the lowest-energy RosettaAntibody homology model produced more accurate predictions than standard rigid-body docking. SnugDock can be combined with ensemble docking to mimic conformer selection and induced fit resulting in increased sampling of diverse antibody conformations. The combined algorithm produced four medium (Critical Assessment of PRediction of Interactions-CAPRI rating) and seven acceptable lowest-interface-energy predictions in a test set of fifteen complexes. Structural analysis shows that diverse paratope conformations are sampled, but docked paratope backbones are not necessarily closer to the crystal structure conformations than the starting homology models. The accuracy of SnugDock predictions suggests a new genre of general docking algorithms with flexible binding interfaces targeted towards making homology models useful for further high-resolution predictions.

Determination of rigid body registration marker error from edge error

Registration markers affixed to rigid bodies (fixed to bone as opposed to skin) are commonly used when tracking 3D rigid body motion. The measured positions of registration markers are subject to unavoidable errors, both systematic and non-systematic. Prior studies have investigated the error propagated to such derived properties as rigid body positions and helical axes, while others have focused on the error associated with a specific position tracking system under restricted conditions. Theoretical and simulation-based error propagation requires knowledge of the variation due to individual registration markers; however, the variation in registration marker position measurement has previously been either assumed or determined from static cases. The objective of this paper is the introduction of a method for determining individual marker variation irrespective of change in rigid body position or motion by utilizing the distances between the markers (edge lengths), which are invariant under rotation and translation. Simulations were used to validate and characterize the introduced technique, demonstrating that the predictions improve with greater edge length and additional markers, converge on reference values where the edge length is at least 4 times the magnitude of the maximum vertex variation, and that under ideal conditions the confidence interval about the predicted variation is within 7% of the maximum variation associated with that marker set. The introduced technique was tested on the results of a motion tracking experiment to demonstrate the wide disparity in vertex variation between static and non-static measurements of the same registration markers, where the non-static variation exceeded the static variation by an average factor of 12.7.

SPHERICAL FOUR-BAR MOTION GENERATION WITH A PRESCRIBED RIGID-BODY LOAD

In motion generation, the objective is to calculate the mechanism parameters required to achieve or approximate a set of prescribed rigid-body positions. This work introduces a new design constraint that considers driving link static torque for a given rigid-body load. By incorporating this new constraint into a conventional spherical four-bar motion generation model [1], spherical four-bar mechanisms are synthesized to achieve-not only prescribed rigid-body positions-but also satisfy a maximum driver static torque for a given rigid-body load.

On adjustable spherical four-bar motion generation for expanded prescribed positions

This work formulates and demonstrates a method to synthesize two-phase adjustable spherical four-bar mechanisms to approximate substantially more prescribed rigid-body positions than with conventional motion generation methods [C.H. Suh, C.W. Radcliffe, Kinematics and Mechanism Design, John Wiley and Sons, New York, 1978]. An alternate set of mechanism constraint equations are formulated using the Method of Least Squares and solved for the adjustable spherical mechanism moving pivot variables. The example included demonstrates the synthesis of an adjustable spherical four-bar mechanism to approximate twice the number of prescribed rigid-body positions per phase than with a conventional method [C.H. Suh, C.W. Radcliffe, Kinematics and Mechanism Design, John Wiley and Sons, New York, 1978].

On Planar Five-bar Motion Generation with a Driver Torque Constraint

In motion generation, the objective is to calculate the mechanism parameters required to achieve or approximate a set of prescribed rigid-body positions. This work introduces a new design constraint that considers driving link static torque for a given rigid-body load. By incorporating this new constraint into a conventional planar five-bar motion generation model, planar five-bar mechanisms are synthesized to not only achieve prescribed rigid-body positions, but also satisfy maximum driver torque for a given rigid-body load.

MULTI-PHASE MOTION GENERATION OF FIVE-BAR MECHANISMS WITH PRESCRIBED RIGID-BODY TOLERANCES

This work presents a technique for synthesizing adjustable planar, five-bar motion generators to approximate prescribed rigid-body positions and satisfy rigid-body positions with prescribed tolerances. This method is an extension of the adjustable planar five-bar motion generation method introduced by the authors (1). By incorporating rigid-body point tolerances in the rigid-body displacement matrices, the calculated circle and center point curves of the five-bar mechanism become circle and/or center point regions. From these regions, fixed and moving pivots for the five-bar mechanism can be selected that approximate the prescribed rigid-body positions and satisfy rigid-body positions with prescribed tolerances. The example in this work considers two-phase moving pivot adjustments in the planar five-bar motion generator.

Design of Adjustable of RSSR-SC Mechanisms for Multi-Phase Motion Generation

This paper presents a technique for synthesizing adjustable RSSR-SC mechanisms to achieve phases of prescribed rigid body positions. The benefit of this method is that RSSR-SC mechanisms can be synthesized to achieve multiple phases of prescribed rigid-body positions using the same hardware. By specifying the joint axes of the C-S and R-S links and establishing perpendicularity between these links and their corresponding joint axes, the constant length condition becomes the only design constraint for these links. The prescribed rigid-body positions are then incorporated in the link constraint Equations with respect to the prescribed coordinate frame for each link and the RSSR-SC mechanism joint variables calculated. The example problem in this work considers a two-phase moving pivot adjustment problem with fixed and adjustable crank and follower lengths.

Kinematic Synthesis of Planar Four-Bar Mechanisms for Multi-phase Motion Generation with Tolerances

This article presents a new technique for synthesizing planar four-bar mechanisms to achieve phases of both precise rigid body positions and rigid body positions with tolerances. This method is an extension of the adjustable RRSS motion generation synthesis methods developed by the authors. (Russell, K., Sodhi R. S. (2001). Kinematic synthesis of adjustable RRSS mechanisms for multi-phase motion generation. Journal of Mechanism and Machine Theory 36:939–952; Russell K., Sodhi R. S. (2002). Kinematic synthesis of adjustable RRSS mechanisms for multi-phase motion generation with tolerances. Journal of Mechanism and Machine Theory 37:279–294.) By incorporating rigid body point tolerances in the rigid body displacement matrices and calculating mechanism fixed and moving pivot solution loci for the prescribed rigid body positions under the tolerance limits, circle and center point regions were calculated. The circle and center points for the crank and follower link solutions for the planar four-bar mechanism were selected from these regions. In this article, two-phase moving pivot adjustment problems with constant crank and follower lengths are considered.

On the design of slider-crank mechanisms. Part I: multi-phase motion generation

A method for designing slider-crank mechanisms to achieve multi-phase motion generation applications typically accomplished by adjustable planar four-bar motion generators is presented. The benefit of this method is twofold. First, multiple phases of prescribed rigid body positions are achievable using a mechanism with fewer moving parts than the planar four-bar mechanism. Second, the slider-crank motion generator can achieve phases of prescribed rigid body positions without any physical or automated adjustments of its moving pivots between phases. A slider path that enables the slider-crank motion generator to achieve two phases of prescribed rigid body positions is designed by using 7th order polynomials to connect the moving pivot paths of the follower link of the adjustable planar four-bar motion generator. This polynomial generates smooth radial displacement, velocity, acceleration and jerk profiles with boundary conditions that can be prescribed. The example problem in this work considers a two-phase moving pivot adjustment of a planar four-bar mechanism.

Kinematic Synthesis of Adjustable RSSR-SS Mechanisms for Multi-Phase Finite and Multiply Separated Positions

This paper presents a new technique for synthesizing RSSR-SS mechanisms to achieve phases of rigid body positions, velocities and accelerations using the same hardware. This work considers two-phase fixed pivot adjustment problems with fixed crank and follower lengths. By specifying the R-S link joint axes, the constant length condition becomes the only design constraint for these links. The prescribed finite and multiply separated positions are then incorporated in the link constraint equations with respect to the prescribed coordinate frame for each link and the RSSR-SS mechanism joint variables and driving link parameters are calculated.

KINEMATIC SYNTHESIS OF RRSC MECHANISMS FOR MULTI-PHASE FINITE AND MULTIPLY SEPARATED POSITIONS

This paper presents a new technique for synthesizing RRSC mechanisms to achieve phases of rigid body positions, velocities and accelerations using the same hardware. This work considers two-phase moving pivot problems with constant R-R and C-S link lengths. By specifying the R-R and C-S link joint axes, the constant length condition becomes the only design constraint for these links. The prescribed finite and multiply separated positions are then incorporated in the link constraint equations with respect to the prescribed coordinate frame for each link and the mechanism joint variables and driving link parameters calculated. The rigid body velocities and accelerations were prescribed using instant screw axis (ISA) parameters.

Study on rigid-body guidance synthesis of planar linkage

In this paper, the guidance-line rotation method of rigid-body guidance is presented. The method effectively solves the rigid-body guidance synthesis problem for the given more than three coupler positions. Using this method, satisfactory four-bar linkages can be obtained such as crank–rocker mechanism, double-rocker mechanism and double-crank mechanism for the given four, five or more than five rigid-body positions. A set of software is developed to realize the automatic design and visualization of guidance synthesis for four-bar linkage, which proves the method to be feasible and effective.

Kinematic synthesis of RRSS mechanisms for multi-phase motion generation with tolerances

This paper presents a new technique for synthesizing spatial RRSS mechanisms to achieve phases of both precise rigid body positions and rigid body positions with tolerances. This method is an extension of the adjustable RRSS motion generation synthesis method developed by the authors [11]. By incorporating rigid body point tolerances in the rigid body displacement matrices and calculating mechanism solution loci for the prescribed rigid body positions under the tolerance limits, circle and center point regions can be calculated. R–R link solutions can then be selected from these regions. This paper considers two-phase fixed and moving pivot adjustment problems with fixed and adjustable crank and follower lengths.

Polynomial Solution of the Spatial Burmester Problem

This paper presents a new method for the dimensional synthesis of the spatial guidance linkage that features the guided body connected to the base by the interposition of five rods having spherical joints at both extremities. The linkage is required to index the guided body through seven arbitrarily-chosen rigid-body positions. Core of the proposed method is an original algebraic elimination procedure that allows five unknowns to be dropped from a set of six second-order algebraic equations in six unknowns. As a result, a final univariate polynomial equation of twentieth order is obtained whose twenty roots, in the complex domain, represent as many possible placements for a connecting rod. A numerical example is reported.

Rationalization of kinematic descriptors for three-dimensional hand and finger motion

Modelling joint motion in three dimensions is often based on techniques taken from classical dynamics, each analysis resulting in a set of six parameters describing the relative motion betwen two body segments. The literature on joint kinematics has been difficult to compare due to use of different anatomical landmarks, axis nomenclature, and analytical methods. It is here shown that with care in sequence definition, the three alignment-based systems (Euler, Cardan, floating axis) give identical results for angular parameters. While the equivalent screw displacement axis system can be related simply to the other methods only if the functional axis of motion is aligned with a coordinate axis, the basic matrix for relating rigid body positions before and after a motion can always be reconstructed. Therefore the changes in alignment angles may be obtained from screw displacement parameters, permitting the results of different analyses to be compared. Translation parameters are most difficult to interpret in any system. Examples of the way in which simple planar motions are characterized by the various analytical methods are given.

Geometric methods for the synthesis of spherical mechanisms for the generation of functions, paths and rigid-body positions using conformal projections

This article briefly reviews the geometric constructions of conformal projections of spherical mechanisms and their components; such as positioning a pair, constructing binary and ternary links, locating coupler points, positioning rigid-bodies, constructing great circles, angles, bisectors, mid-normals, and less-circles. Then, it presents the methods, and constructions for the synthesis of spherical mechanisms for function generation using pole, inversion, and overlay techniques; and for spherical path and rigid-body position generation using pole techniques. Syntheses of the spherical slider-crank, spherical crank-rocker and spherical cam-follower mechanisms are also included. These very simple geometric synthesis techniques are illustrated with numerical examples. Analytical expressions for each geometric construction are given for computer aided solutions on the projection plane and then transfer the solution into the inertial reference system.