Instantaneous Screw Axis Research Articles

High-speed, three-dimensional kinematic analysis of the normal wrist

Carpal kinematics during a wrist flexion/extension motion using high-speed videodata acquisition was investigated. A cadaver forearm was stabilized, allowing unconstrained excursion of the wrist for passive range of motion (ROM). The extensor and flexor pairs of the wrist were looped together and a 1-lb weight was attached to each pair, simulating synergistic muscle tension. Capitate/radius and third metacarpal/radius angles were calculated to determine which measurement would be best for determining global wrist angle. The average difference in capitate/radius and third metacarpal/radius angles at each respective flexion/extension wrist angle for all wrists was 1.1 degrees +/- 1.6 degrees (the maximum difference was 4 degrees). Hence, the capitate-third metacarpal joint can be considered rigid. Capitate/lunate motion as described by capitate-radius Euler angles ranged from -16.9 to 23.5 with total capitate/lunate motion of 40.5 (35%) in the 114 degrees total global wrist ROM measured. Radius/lunate motion as described by lunate-radius angle ranged from -8.2 to 48.4 with total radius/lunate motion of 56.5 (49%) in the 114 degrees total global wrist ROM measured. During global wrist motion, the radiolunate joint contributes more motion in flexion than the capitolunate joint and the capitolunate joint contributes more motion in extension than the radiolunate joint. The instantaneous screw axes (ISAs) were calculated for each third metacarpal position with respect to the radius. The average distance difference between ISAs for the 4 wrists tested was -1.23 +/- 14.97 pixels. The maximum distance was 56.51 pixels and the minimum was -24.09 pixels. This new combination of motion analysis and 3-dimensional reconstructions of computed tomography images affords a high-speed, dynamic analysis of kinematics. It shows that during wrist flexion/extension, normal carpal kinematics does not have an ISA fixed in or limited to the capitate. In addition, the ISA data provide evidence that translational motion is a real and measurable component of normal carpal motion. These findings alter the understanding of carpal kinematics obtained from the results of previous studies which suggested that the center of rotation was fixed in the capitate.

Use of swept volumes in the design of interference free spatial mechanisms

Geometric modeling of a moving object (a generator) depends on two factors: its geometry and motion characteristics. The resulting model is commonly called the swept volume. In this study, geometries of the generators are represented by natural quadric surfaces (planes, circular cylinders, circular cones and spheres). Meanwhile, the instantaneous screw axis is used to describe the sweep motion of the generators and to aid the construction of their swept volumes. A closed formed solution to determine the points on the boundary of a swept volume at a specific time is developed for each of the generators. A point set which contains these points is called the characteristic curve. The final swept volume of a generator is a faceted model from a set of characteristic curves at different time steps over a time domain within which it moves. In this paper, the application of swept volumes in the geometric design of spatial mechanisms is discussed.

NORMAL WRIST KINEMATICS AND THE ANALYSIS OF THE EFFECT OF VARIOUS DYNAMIC EXTERNAL FIXATORS FOR TREATMENT OF DISTAL RADIUS FRACTURES

The purpose of this study was to evaluate the effect that external fixation devices used for distal radius fractures have on normal carpal kinematics, using high speed video data acquisition. Cadaver forearms were stabilized, allowing free excursion of the wrist for passive range of motion. Synergistic muscle tension was simulated by looping the extensor and flexor pairs of the wrist. Global wrist flexion and extension, intercarpal angles, and the instantaneous screw axis (ISA) were studied. These parameters allowed a quantification of normal carpal kinematics and comparison to the kinematics of the carpal bones with external fixators attached. This study shows that normal carpal kinematics during wrist flexion and extension do not have an ISA fixed in or limited to the capitate. In addition, the ISA data provide evidence that translational motion is a real and measurable component of normal carpal motion. This would change the understanding of carpal kinematics in previous studies that suggested that the center of rotation was fixed in the capitate. The proximal carpal (radiolunate) joint contributes more motion (has a greater rotation angle) in normal global wrist flexion and the midcarpal (capitolunate) joint contributes more motion in normal global wrist extension. In addition, the global range of motion and intercarpal joint angle of the wrist are limited with the application of any of the external fixators tested. None of the external fixators allowed normal ISA vector surfaces during wrist motion.

LOAD MECHANICS OF THE WRIST

During the last decade, we have been studying load mechanics under a variety of conditions using pressure-sensitive film and, more recently, three-dimensional reconstructions and motion analysis. In all of these studies using pressure-sensitive film, the simulated pathologic or traumatic conditions that were tested showed that all areas in which an increase in contact area or pressure occurred, localized to one area of one joint, coincided with areas in which degenerative changes occurred in the simulated clinical situation. The areas in which there was a decrease or no change in contact area or pressure coincided with areas that were spared from degenerative changes in simulated clinical situations. More recent work has demonstrated that normal carpal kinematics during wrist flexion and extension do not have an instantaneous screw axis that is fixed in or limited to the capitate. These findings change the understanding previously based on studies suggesting that the center of rotation was fixed in the capitate. It was noted that during global wrist motion the radiolunate joint contributes more motion and flexion than the capitolunate joint, but the capitolunate joint contributes more motion and extension than the radiolunate joint. It also was demonstrated that translational motion is a normal component of carpal kinematics.

Kinematic Analysis of RSCR Spatial Four-Link Mechanisms.

The formulas for displacement and velocity analyses are derived for a spatial four-link mechanism with two revolute pairs, a spherical pair and a cylindrical pair. Then, a procedure for determining instantaneous screw axes is presented and their behaviors in the neighborhood of limit positions are clarified. The condition for limit positions of the driving-link motion is obtained on the basis of force transmission from the coupler link to the driven link and the determinant composed of the coefficients of simultaneous equation for velocity analysis. The conditional function is investigated geometrically and a quantity is proposed in order to evaluate motion and force transmission characteristics.

Swept volumes generated by the natural quadric surfaces

The swept volume of a moving object (generator) can be constructed from the envelope surfaces of its boundary. These envelope surfaces are the collections of the characteristic curves which are the point sets on the boundary of the generator at different times. In this study, the characteristic curves of the natural quadric surfaces (planes, circular cylinders, circular cones and spheres) are derived from the envelope theorem. The instantaneous screw axis is used to describe the sweep motion of the generators and to solve the characteristic curves. The faceted model of a swept volume is then established by warping the corresponding characteristic curves together with the partial bouncaries of the generator at the initial and final positions.

Kinematic and Static Characteristics of In-parallel Actuated Manipulators at Singular Points and in Their Neighborhood

In the process of mechanism design and trajectory planning of in-parallel actuated manipulators, it is necessary to know the locations of all singular points in the working space. We propose a new method for numerically locating the singular points of in-parallel actuated manipulators based on the pressure angle. A singular-point curve is defined as a set of singular points. Kinematic and static characteristics at singular points are analyzed by pressure angles and instantaneous screw axes. Singular points of the Stewart Platform are investigated using the proposed method. The neighborhood of singular points is determined from output error, isotropy of output force and driving force, and thus the practical working space is defined.

Kinematic and Static Characteristics of In-parallel Actuated Manipulators at Singular Points and in their Neighborhoods.

In the process of mechanism design and trajectory planning of in-parallel actuated manipulators, it is necessary to grasp the locations of all of singular points in the working space. This paper proposes a new method for numerically searching for the singular points of in-parallel actuated manipulators based on the pressure angle. A singular-point curve is defined as a set of singular points. Since the working space is divided into multiple regions by the singular-point curves, the end-effector cannot move freely from one region to any other regions. Kinematic and static characteristics at singular points are analyzed by pressure angles and instantaneous screw axes. Singular points of the Stewart-Platform are investigated based on the proposed method. Characteristics in the neighborhoods of singular points are analyzed from the points of view of output error, isotropy of output force and driving force, and the practical working space is defined.

Determination of First and Second Order Instant Screw Parameters from Landmark Trajectories

Least squares methods were developed to determine instant screw axis (ISA) and angular acceleration axis (AAA) parameters in experimental and analytical studies. The algorithms provide linear relationships for rigid body velocity and acceleration descriptors based on position, velocity, and acceleration data for individual points on the body. Weighted least squares estimators are presented for statistical weighting on individual landmarks as well as for variance weighting to reduce systematic measurement effects. The methods include instantaneous second order screw motion which describes differential geometry of screw axodes. Two spatial mechanism examples provide recommendations for landmark count, distribution, and placement.

Spatial motion-I: Points of inflection and the differential geometry of screws

This paper examines infinitesimal spatial motion, introducing the concept of a “differential screw” to characterize the difference between two successive instantaneous screw axes (ISAs) on an axode. The locus of spatial inflection points, a twisted cubic curve common to three ruled quadric surfaces, is here derived in a coordinate system attached to the fixed axode, using the relationships of the ISA to velocity and the differential screw, as well as the ISA, to acceleration. The notable geometry is then discussed, and the more familiar instances of spherical and planar motion are described as special cases. The novel approach adopted in this paper, even though it does not yield any new results, is essential in laying the groundwork for Part II [ Mech. Mach. Theory 27, 17–35 (1992)] that deals with accelerations and the spatial equivalent of the Bresse circle.

Kinematische geometrie der axoiden und die bahnfläche einer geraden

It is known that any motion is characterized instantaneously by the instantaneous screw axis. This present work is concerned with the properties that follow from a study of the screw axis and the shapes of the axodes. Known results are derived together with some new results. During the general motion of two bodies the instantaneous screw axis changes its position and properties and generates two different but related ruled surfaces in the respective members, called the fixed axode in the fixed member, and the moving axode in the moving member. During the motion the axodes roll and slide on each other in a special way such that tangential contact between the axodes is always maintained along the entire length of the mating generators which together determine the instantaneous screw axis at any instant. The two successive moving screws share with the two fixed ones the same common perpendicular and they also share the same angle of inclination with respect to one another. A line of moving axoides in general generates a ruled surface. In the second part of this work is given a systematic of such ruled surfaces (axodes) on the basis of four invariants. In a previous work[1] similar problems about axodes and the path of the axodes were treated analytically.

Force distribution in closed kinematic chains

The problem of force distribution in systems involving multiple frictional contacts between actively coordinated mechanisms and passive objects is examined. The special case in which the contact interaction can be modeled by three components of forces (zero moments) is particularly interesting. The Moore-Penrose generalized inverse solution for such a model (point contact) is shown to yield a solution vector such that the difference between the forces at any two contact points projected along the line joining the two points vanishes. Such a system of contact forces is described by a helicoidal vector field which is geometrically similar to the velocity field in a rigid body twisting about an instantaneous screw axis. A method to determine this force system is presented. The possibility of superposing another force field which constitutes the null system is also investigated.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Instantaneous Kinematics of Three-Parameter Motions

In this paper we study the instantaneous kinematics of a three-link open-chain system. We derive concise closed-form expressions to determine the angular velocity, the pitch, and the instantaneous screw axis that describe the three-parameter motion of the terminal link of the three-link chain relative to the fixed base. Using two joint angular velocity ratios as variable parameters we interpret the double-infinity of solutions as a family of cylindroids. For illustrative purposes, we present an analysis of the arm subassembly of two well-known robot manipulators.

Instantaneous Kinematics of a Special Two-Parameter Motion

In this paper, the author studies the instantaneous kinematics of a rigid body when it is guided by a revolute-revolute crank. It is shown that the locus of the instantaneous screw axes is a cylindroid and the locus of all the parabolic points is a plane and a fifth order surface.

Screw axes and mobility in spatial mechanisms via the linear complex

The geometry of the linear complex, as an expression of the helicoidal field of relative infinitesimal displacements of two bodies, is used to determine instantaneous screw axes in spatial mechanisms. It is then shown how the existence of many over-constrained linkages can be explainedm and even predicted, by applying simple theorems directly related to linear complexes, congruences, and ruled quadric surfaces.

Prismatic pairs in spatial linkages

A partial survey is made of spatial linkages containing prismatic (sliding) pairs, concentrating mainly on linkages that have mobility equal to one and yet do not comply with the general form of Kutzbach's Mobility Criterion. The mobility of the special linkages investigated is determined by establishing, for a general configuration, the unique locations of certain instantaneous screw axes. Some of the linkages that are revealed are thought to be new. Some coincide with linkages that have been discovered before by different and more laborious techniques.

Acceleration Analysis of Spatial Linkages Using Axodes and the Instantaneous Screw Axis

The application of recent techniques developed in the geometry and the kinematics of instantaneous spatial motion generated by a pair of axodes, and the relative spatial motion of three rigid bodies using the instantaneous screw axis is demonstrated in an analysis of the Bennett Mechanism. Explicit equations which are well suited to machine calculations yield input-output information, the location and the properties of the instantaneous screw axis, the characteristic properties of the axodes, the velocity and the acceleration of a general point in the moving link, and the position of the center of acceleration in the moving link.

The constraint analysis of mechanisms

A general method for the determination of the mobility of any rigid body mechanism is derived using Ball's theory of the instantaneous screw axis. The classical mobility equations are related to this method and their limitations are elucidated. A relationship between the reciprocal screw systems of the joints of a mechanism and the number of accurate operations required in the manufacture of a machine based on that mechanism is described.