Morphometrics is a quantitative analysis to compare a set of geometric representations of forms, including shape and size. Analysis of shape variation is useful in systematics, evolutionary biology, biostratigraphy, and developmental... more
Morphometrics is a quantitative analysis to compare a set of geometric representations of forms, including shape and size. Analysis of shape variation is useful in systematics, evolutionary biology, biostratigraphy, and developmental biology. Distinguished by the data being analyzed, three forms of morphometrics are commonly recognized. Traditional morphometrics measures the lengths, ratios, angles, etc., of patterns of shape variations. Outline-based morphometrics analyzes the outlines of forms using open or closed curves. Landmark-based geometric morphometrics summarizes shapes in terms of the coordinates of anatomical landmarks. The three morphometric methods are able to capture the variation of forms exactly, but require analyzing numerous variables. As an alternative approach to morphometrics, this paper presents a kinematic synthesis methodology of planar rigid-body chains. This methodology approximates the set of profile curves that represent a series of shapes with a single chain comprised of rigid-body links connected by revolute or prismatic joints. The primary advantage of the presented approach is that a modest number of physical parameters describes the shape and size change between a set of curves. Three morphometric problems are investigated by applying the methodology of synthesizing planar rigid-body chains to match the prescribed shapes. The result validates that the presented methodology might be used as an alternative approach to the analysis of morphological forms.
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This paper presents a mechanism design optimization for actuating the horizontal stabilizers of an aircraft using a rotating empennage without a vertical stabilizer. Birds do not have vertical stabilizers and rotate their tail feathers to... more
This paper presents a mechanism design optimization for actuating the horizontal stabilizers of an aircraft using a rotating empennage without a vertical stabilizer. Birds do not have vertical stabilizers and rotate their tail feathers to control agile maneuvers. A rotating empennage concept will mimic this motion and enable the bio-inspired flight of a fixed wing aircraft. To maintain control, the bioinspired rotating empennage (BIRE) will incorporate three degrees of freedom: independent rotation of each horizontal stabilizer and rotation of the empennage relative to the main axis of the fuselage. The primary benefits of an aircraft without a vertical stabilizer are reduced drag and weight which, in turn, results in more efficient operation. In order to reduce inertia of the rotating empennage, the linear actuators that position the horizontal stabilizers will be placed within the fuselage. Mechanisms that couple the linear translation of the actuators with the rotation of the horizontal stabilizers ideally require a low peak force and short stroke from the actuator. With two conflicting objectives, a Pareto front optimization was conducted to determine appropriate link lengths of candidate solutions and to understand the effectiveness of alternate mechanisms. The study considers rack & pinon, scotch-yoke, slider-crank, inverted slider-crank, Watt II, and Stephenson III mechanisms.
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This paper presents the use of a geared five-bar with connecting rod and sliding output for mechanical presses. Mechanical presses are used to form sheet metal parts and have economical benefits to other presswork production methods. A... more
This paper presents the use of a geared five-bar with connecting rod and sliding output for mechanical presses. Mechanical presses are used to form sheet metal parts and have economical benefits to other presswork production methods. A conventional mechanical press is driven with a slider-crank mechanism. Extended drive presses are used to alter the stamping motion required for certain operations. For instance, certain coining and squeezing operations prefer a long dwell. A knuckle joint mechanism is commercially available and permits some control over the output motion. A synthesis process is developed in this paper to produce a prolonged dwell and is applied to the kuckle joint mechanism. The geared five-bar with sliding output is shown to produce a longer dwell than a knuckle joint mechanism.
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This paper presents a mechanism design optimization for actuating the horizontal stabilizers of an aircraft using a rotating empennage without a vertical stabilizer. Birds do not have vertical stabilizers and rotate their tail feathers to... more
This paper presents a mechanism design optimization for actuating the horizontal stabilizers of an aircraft using a rotating empennage without a vertical stabilizer. Birds do not have vertical stabilizers and rotate their tail feathers to control agile maneuvers. A rotating empennage concept will mimic this motion and enable the bio-inspired flight of a fixed wing aircraft. To maintain control, the bio-inspired rotating empennage (BIRE) will incorporate three degrees of freedom: independent rotation of each horizontal stabilizer and rotation of the empennage relative to the main axis of the fuselage. The primary benefits of an aircraft without a vertical stabilizer is reduced drag and weight, which in turn results in more efficient operation. In order to reduce inertia of the rotating empennage, the linear actuators that position the horizontal stabilizers will be placed within the fuselage. Mechanisms that couple the linear translation of the actuators with the rotation of the horizontal stabilizers ideally require a low peak force and short stroke from the actuator. With two conflicting objectives, a Pareto front optimization was conducted to determine appropriate link lengths of candidate solutions and to understand the effectiveness of alternate mechanisms. The study considers a rack & pinon, scotch-yoke, slider-crank, inverted slider-crank, Watt, and Stephenson mechanisms.
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This paper approaches the type synthesis of multi-degree of freedom planar metamorphic mechanisms with a single driver in a systematic process. The process is facilitated by implementing a constraint status matrix and a equivalent... more
This paper approaches the type synthesis of multi-degree of freedom planar metamorphic mechanisms with a single driver in a systematic process. The process is facilitated by implementing a constraint status matrix and a equivalent resistance matrix as a method for identifying an appropriate structure of planar metamorphic mechanisms with a single driver. Multi-structures can be obtained from the same source metamorphic mechanism by designing different constraint architectures of metamorphic joints. To determine the constraint architectures of metamorphic joints and their different assembly combinations, the constraint status matrix is built based on the task-based metamorphic cyclogram of a source mechanism. According to the equivalent resistance gradient model and the constraint status matrix, an equivalent resistance matrix for the metamorphic joints is proposed. A structural synthesis matrix of the metamorphic mechanism is then obtained from the equivalent resistance matrix by deducing the constraint-form vectors of the metamorphic joints. Furthermore, an effective kinematic diagram synthesis of the source mechanism of the planar metamorphic mechanism is proposed which is based only on the 14 one or zero degree-of-freedom (DOF) linkage groups. The entire structural design method of a metamorphic mechanism is based on the structural synthesis matrix and given in steps. Finally, a proposed structural design approach is illustrated by two examples.
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The fixed pivots of a planar 4R linkage that can achieve four design positions are constrained to a center-point curve. The curve is a circular cubic function and plots can take one of five different forms. The center-point curve can be... more
The fixed pivots of a planar 4R linkage that can achieve four design positions are constrained to a center-point curve. The curve is a circular cubic function and plots can take one of five different forms. The center-point curve can be generated with a compatibility linkage obtained from an opposite pole quadrilateral of the four design positions. This paper presents a method to identify design positions that generate distinctive shapes of the center-point curves. The form of the center-point curve is dependent on whether the shape of the opposite pole quadrilateral is an open or closed form of a rhombus, kite, parallelogram, or when the sum of two sides equals the other two. Interesting cases of three and five position synthesis are also explored. Four and five position cases are generated that have center points at infinity allowing a PR dyad with line of slide in any direction to achieve the design positions. Further, a center-point curve for five specific design positions is revealed.
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Any articulated system of rigid bodies defines a statically equivalent serial chain (SESC). The SESC is a virtual chain that terminates at the center of mass (CoM) of the original system of bodies. An SESC may be generated experimentally... more
Any articulated system of rigid bodies defines a statically equivalent serial chain (SESC). The SESC is a virtual chain that terminates at the center of mass (CoM) of the original system of bodies. An SESC may be generated experimentally without knowing the mass, CoM, or length of each link in the system given that its joint angles and overall CoM may be measured. This paper presents three developments toward recognizing the SESC as a practical modeling technique. Two of the three developments improve utilizing the technique in practical applications where the arrangement of the joints impacts the derivation of the SESC. The final development provides insight into the number of poses needed to create a usable SESC in the presence of data collection errors. First, modifications to a matrix necessary in computing the SESC are proposed, followed by the experimental validation of SESC modeling. Second, the problem of generating an SESC experimentally when the system of bodies includes a mass fixed in the ground frame are presented and a remedy is proposed for humanoid-like systems. Third, an investigation of the error of the experimental SESC versus the number of data readings collected in the presence of errors in joint readings and CoM data is conducted. By conducting the method on three different systems with various levels of data error, a general form of the function for estimating the error of the experimental SESC is proposed.
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This work seeks to systematically model and solve the equations associated with the kinematics of spherical mechanisms. The group of special unitary matrices, SU(2), is utilized throughout. Elements of SU(2) are employed here to analyze... more
This work seeks to systematically model and solve the equations associated with the kinematics of spherical mechanisms. The group of special unitary matrices, SU(2), is utilized throughout. Elements of SU(2) are employed here to analyze the three-roll wrist and the spherical Watt I linkage. Additionally, the five orientation synthesis of a spherical four-bar mechanism is solved, and solutions are found for the eight orientation synthesis of the Watt I linkage. Using SU(2) readily allows for the use of a homotopy-continuation-based solver, in this case Bertini. The use of Bertini is motivated by its capacity to calculate every solution to a design problem.
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This work investigates the kinematic synthesis methodology for designing a chain of three-dimensional bodies to match a set of arbitrary spatial curves. The bodies synthesized can be one of three types: a rigid segment, a helical segment... more
This work investigates the kinematic synthesis methodology for designing a chain of three-dimensional bodies to match a set of arbitrary spatial curves. The bodies synthesized can be one of three types: a rigid segment, a helical segment with constant curvature and torsion but varying length, and a growth segment that maintains its geometry but may be scaled to become larger or smaller. To realize mechanical chains, only rigid and helical segments are used. After designing the segments, they may be aligned with the original spatial curves with their ends connected via an optimization. For two curves, these connections may be made with revolute joints to obtain high accuracy. For three or more curves, spherical joint connections allow for the best accuracy. To compare curves as is useful in morphometry, all three segment types may be employed. In this case, an accurate description of the changes between curves is important, and optimizing to connect the segments is not needed. The procedure for redefining the curves in a way that the techniques in this paper may be applied, as well as the methodologies for synthesizing the three segment types are presented. Examples include a continuum robot problem and the morphometric analyses of chochlear curves and the lambdoidal suture. This work extends the established planar techniques for synthesizing mechanisms and addressing morphometric issues that are motivated with curves in two-dimensions.
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This paper presents a study on the energy utilization of planar automation mechanisms that operate with controlled moves. Designers of factory automation for pick & place tasks often select multiple degree-of-freedom robotic devices.... more
This paper presents a study on the energy utilization of planar automation mechanisms that operate with controlled moves. Designers of factory automation for pick & place tasks often select multiple degree-of-freedom robotic devices. With multiple degrees-of-freedom, task flexibility is available, but many operations require little or no flexibility. The majority of research on the energy usage of these robot devices for pick & place tasks focuses on path planning. The study presented in this paper explores the energy savings in using low degree-of-freedom devices and the influence of design parameter selection. Energy predictor equations are developed and confirmed through experimentation. Various positioning mechanisms of differing dimensions are studied for trends in energy utilization. Lastly, an actuator control strategy is proposed for further reducing energy requirements. The study concludes that energy usage can be substantially decreased in pick & place applications by reducing the degrees of freedom of the device, implementing a prudent mechanism architecture, ideally selecting mechanism dimensions and optimally controlling the actuator(s).
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In this paper we present a methodology for determining the link dimensions of a two-actuator device capable of guiding a part through two specified spatial positions. In addition, the device must be capable of producing two specified... more
In this paper we present a methodology for determining the link dimensions of a two-actuator device capable of guiding a part through two specified spatial positions. In addition, the device must be capable of producing two specified linear velocities, one at each spatial position. This represents a spatial pick-and-place operation with a fixture holding the part at both ends. The device we seek to dimension is a spherical four-bar mechanism mounted on a prismatic joint. In order to achieve the specified positions and velocities, we assume the following actuation scheme. The spherical four-bar is actuated to start the motion from the first position, then moves in tandem with the prismatic joint. The prismatic joint completes its slide, and then the spherical four-bar aligns the body with the second position. An example of the methodology is shown.
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This paper presents a topology optimization methodology to synthesize cable-actuated, shape-changing, tensegrity systems specified through path generation requirements. Estabished tensegrity topology optimization procedures exist for... more
This paper presents a topology optimization methodology to synthesize cable-actuated, shape-changing, tensegrity systems specified through path generation requirements. Estabished tensegrity topology optimization procedures exist for static structures. For active tensegrity systems, motion characteristics are typically explored after the structural topology is determined. The work presented in this paper extends the established procedure to introduce prescribed motion into the topology optimization. A ground structure approach is used in conjunction with the design space. The topology optimization problem is formulated into a mixed integer linear programming problem. Desired motion is prescribed by identifying trace points in the design space and corresponding paths. The result of this methodology is the creation of a tensegrity system that can achieve shape-change as specified with prescribed paths.
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ABSTRACT The identification of motion characteristics and assembly circuits is fundamental in creating a workable mechanism. A circuit defect prevents a mechanism from moving between de-sired positions. This paper extends the established... more
ABSTRACT The identification of motion characteristics and assembly circuits is fundamental in creating a workable mechanism. A circuit defect prevents a mechanism from moving between de-sired positions. This paper extends the established methods for analyzing multi-degree-of-freedom platforms to gain insight on single-actuated linkages. Specifically, from a plot of the singu-larity locus projected onto the input joint space, the number of singularities, number of geometric inversions and circuit regimes are revealed. The input/output motion of the linkage can be in-ferred from the locus. The methodology to produce the singu-larity locus is general and does not rely on geometric insights of a particular mechanism. By using the locus, desired operational features can be readily identified, such as a fully rotatable crank. Unique motion characteristics, such as a greater than 360 • non-rotatable crank, can be also be detected. Further, it is observed that transition linkages serve as bounds between the regions of circuit change. 1 INTRODUCTION Forward kinematic position analysis of a mechanism in-volves determining the position and orientation of links as an input link(s) is actuated. Since the governing position equations for the links in a mechanism are non-linear, multiple solutions are obtained for a single position of the input link(s). These differ-ent solutions or various configurations of a mechanism are called geometric inversions (GIs) [1]. For a specific mechanism, the number of GIs is dependent on the position of the input link(s).
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This paper presents the development of variable geometry dies that enable the extrusion of plastic parts with a varying cross section. Extrusion accounts for 40% of all manufactured plastic parts because it is a relatively low-cost and... more
This paper presents the development of variable geometry dies that enable the extrusion of plastic parts with a varying cross section. Extrusion accounts for 40% of all manufactured plastic parts because it is a relatively low-cost and high-production-rate process. Conventional polymer extrusion technology, however, is limited to fixed dies that produce continuous plastic products of constant cross section defined by the die exit profile. A shape-changing die allows the cross section of the extruded part to change over its length, thereby introducing the capacity to manufacture plastic faster and with lower tooling costs than injection molding. This paper discusses design guidelines that were developed for movable die features including revolute and prismatic joint details, land length, and the management of die leakage. To assess these guidelines, multiple dies have been designed and constructed to include an arbitrary four-sided exit profile where changes were made to the internal angles and length of sides as the extruder was operating. Experimental studies were conducted by using different extruder line settings and time between die movements. Test results are presented that include shape repeatability and the relationship between extrudate profile and die exit geometry.
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ABSTRACT Synthesizing a motion generating 3-jointed planar chain, under no additional constraints, is trivial. Given a set of desired planar rigid body positions, one can select via straightforward geometric considerations the locations... more
ABSTRACT Synthesizing a motion generating 3-jointed planar chain, under no additional constraints, is trivial. Given a set of desired planar rigid body positions, one can select via straightforward geometric considerations the locations of the revolute (R) joints and prismatic (P) joints of a chain that will reach the positions. On the other hand, specifying constraints on joint limitations or physical parameters may result in no chains that reach the desired positions. In this paper, we study a rigid body in a set of positions in order to determine the point on the body that lies nearest a point, circle or line. Note that the point, circle or line is unknown and is determined as part of the process. The set of points formed by the rigid body point in all of its positions defines a workspace for the outermost moving pivot of the chain. By fitting a generic RPR, PRR or RRR chain’s workspace to these points, we can suggest nearly minimal joint constraints and physical parameters.
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A coupler-driver for a planar mechanism is a revolute-prismatic-revolute (RPR) chain connected between ground and one of the links of the mechanism. The focus of this work is to investigate how the use of a coupler-driver as the source of... more
A coupler-driver for a planar mechanism is a revolute-prismatic-revolute (RPR) chain connected between ground and one of the links of the mechanism. The focus of this work is to investigate how the use of a coupler-driver as the source of actuation alters the set of solutions for a four position task by avoiding defects relative to the joints of the actuated mechanism. Type maps are a synthesis tool used to visualize the solutions for the four position task, which previous researchers have used to identify the mechanism class and the ability to actuate each solution through the task. This work extends the type map concept to represent the number of solutions to a four position task that are drivable via either a coupler-driver or an input torque at one of the fixed joints. The use of a coupler-driver as the actuator is found to allow many mechanisms that suffer from a branch defect relative to the joints of the kinematic solution mechanism to be valid solutions. For the example four position tasks tested, the coupler-driver was found to expand the number of four-bar mechanism solutions. As part of this analysis, a variation of the derivation of the space of fixed and moving pivot pairs that produce a coupler-driver capable of actuating a single degree of freedom planar mechanism is presented.
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This paper presents a new method for determining whether an RR dyad will pass through a set of finitely separated positions in order. Several established solution methods have been previously documented for this problem. This method... more
This paper presents a new method for determining whether an RR dyad will pass through a set of finitely separated positions in order. Several established solution methods have been previously documented for this problem. This method utilizes only the displacement poles in the fixed frame to assess in an intuitive fashion whether a selected fixed pivot location will result in an ordered dyad solution. A line passing through the selected fixed pivot is rotated one-half revolution about the fixed pivot, in a manner similar to a propeller with infinitely long blades, to sweep the entire plane. Order is established by tracking the sequence of the displacement poles intersected by the rotating line. With four or five positions, fixed pivot locations corresponding to dyads having any specified order are readily found. Five-position problems can be directly evaluated to determine if any ordered solutions exist, and degenerate cases of four positions for which the set of fixed pivots corresponding to ordered dyads collapses to a single point on the center point curve can be identified.
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This work presents a comparison between two actuation methods for planar and spherical four-bar mechanisms. The first is actuation by a torque applied at either of the fixed pivots. The second actuation method uses a linear actuator... more
This work presents a comparison between two actuation methods for planar and spherical four-bar mechanisms. The first is actuation by a torque applied at either of the fixed pivots. The second actuation method uses a linear actuator connected between ground and the coupler. For any four position task, planar or spherical, a one parameter set of dyads is found that may be used to guide the body through the four positions. Any two of these dyads, when coupled, define a potential four-bar solution to the task. A sampling across the set of all possible mechanisms that solve the four position task may be compared by analyzing the internal static loads of the four-bar mechanisms. The comparison was conducted to determine if coupler-driven four-bars have reduced internal loading when compared to torque-driven mechanisms. Four position tasks were used for comparison of mechanisms designed for the same task, under the assumption that the optimal torque-driven mechanism would have a different set of kinematic parameters than the optimal coupler-driven mechanism.
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This paper presents an investigation of a mechanism to improve the power throughput of persons with tetra- or paraplegia pedaling via functional electrical stimulation (FES). FES stimulates muscle contraction with small electrical... more
This paper presents an investigation of a mechanism to improve the power throughput of persons with tetra- or paraplegia pedaling via functional electrical stimulation (FES). FES stimulates muscle contraction with small electrical currents and has proven useful in building muscle in patients while relieving soreness and promoting cardiovascular health. An FES-stimulated cyclist produces power that is an order of magnitude less than an able-bodied cyclist. At these reduced power levels, many difficulties associated with FES cycling become apparent, namely inactive zones. Inactive zones are defined by the leg being in a position where muscle stimulation is unable to produce power to propel the tricycle forward. A possibility for reducing inactive zones and increasing the power throughput of the cyclist is to alter the motion of a cyclist’s legs. Bicycles have recently been marketed that feature pedaling mechanisms that employ alternate leg motions. This work considers using a four-bar and ratchet-and-pawl linkage in the redesign of a performance tricycle piloted by an FES-stimulated rider. Quasi-static and power models have been optimized for this cycling architecture yielding a design that suggests a 79% increase in throughput power for some FES cyclists. Multiple sets of dimensions are compared against design criteria to identify an ideal design.
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This paper presents a kinematic synthesis methodology for planar shape-changing rigid-body mechanisms that addresses constraints arising in the design of variable-geometry polymer extrusion dies. Such a die is capable of morphing its... more
This paper presents a kinematic synthesis methodology for planar shape-changing rigid-body mechanisms that addresses constraints arising in the design of variable-geometry polymer extrusion dies. Such a die is capable of morphing its orifice in order to create extrusions of non-constant cross section. A variable-geometry shape-changing die problem is defined by a set of design profiles of different shapes and arc lengths, which approximate various cross sections of the extrusion. The primary advantage of the presented methodology is addressing the need for bodies in the mechanism formed by fusing links in the shape-changing portion of the chain. Previous methodologies included such fused links, but only at the end of the synthesis process where revolute joints were seen to be underutilized. A new method is needed to control, or even eliminate the use of revolute joints in the shape-changing chain of rigid links. The result of this new work is an iterative method which generates an optimized morphing chain to best match the design profiles while minimizing the number of prismatic and revolute joints needed to do so. The additional variable-geometry design constraints also require a generalization to the definition of fixed-end profiles previously proposed, also allowing chain ends to be defined by prismatic joints on a fixed line of slide. A virtual-chain method is also proposed to solve closure problems caused by the reduction in the number of revolute joints.Copyright © 2015 by ASME
Research Interests: Engineering and Morphing
This paper presents an analysis to create a general singularity condition for a mechanism that contains a deformable closed contour. This kinematic architecture is particularly relevant to rigid-link, shape-changing mechanisms. Closed... more
This paper presents an analysis to create a general singularity condition for a mechanism that contains a deformable closed contour. This kinematic architecture is particularly relevant to rigid-link, shape-changing mechanisms. Closed contour shape-changing mechanisms will be shown to belong to the Assur classification because of the pattern of interconnections among the links. The general singularity equations are reduced to a condensed form, which allows geometric relationships to be readily detected. The analysis is repeated for alternative input links. A method for formulating the singularity condition for an Assur Class N, knowing the condition for a Class N−1 mechanism, is given. This approach is illustrated with several examples.
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A linkage is partially classified by identifying those links capable of unceasing and drivable rotation and those that are not. In this paper, we examine several planar single degree-of-freedom linkages to identify all changes to the... more
A linkage is partially classified by identifying those links capable of unceasing and drivable rotation and those that are not. In this paper, we examine several planar single degree-of-freedom linkages to identify all changes to the physical parameters that may alter this classification. The limits on the physical parameters that result in no change in the classification are defined by transition linkages. More rigorously, a transition linkage possesses a configuration at which the matrix defined by the derivative of the loop closure equations with respect to the joint variables loses rank. Transition linkages divide the set of all linkages into different classifications. In the simplest cases studied, transition linkage identification produces a comprehensive classification scheme. In all cases, this identification is used to alter a linkage’s physical parameters without changing its classification and produces insight into the selection of these parameters to produce a desired classification.
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This paper extends the kinematic synthesis methodology for designing a chain of bodies to match a set of arbitrary curves to the spatial case. The methodology initiates with an arbitrary set of spatial curves, and concludes with a set of... more
This paper extends the kinematic synthesis methodology for designing a chain of bodies to match a set of arbitrary curves to the spatial case. The methodology initiates with an arbitrary set of spatial curves, and concludes with a set of bodies defined by their spatial features. The bodies synthesized can be one of three types: a rigid segment, a helical segment with constant curvature and torsion but varying length, and a growth segment that maintains its geometry but may be scaled to become larger or smaller. To realize mechanical chains for mechanisms that achieve spatial shape change, only rigid and helical segments are used. After designing the segments, they may be aligned with the original spatial curves with their ends connected via an optimization. For two curves, these connections may be made with revolute joints to obtain high accuracy. For three or more curves, spherical joint connections allow for best accuracy. To compare curves as is useful in morphometry, all three s...
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This work seeks to systematically model and solve the equations associated with the kinematics of spherical mechanisms. The group of special unitary matrices, SU(2), is utilized throughout. Elements of SU(2) are employed here to analyze... more
This work seeks to systematically model and solve the equations associated with the kinematics of spherical mechanisms. The group of special unitary matrices, SU(2), is utilized throughout. Elements of SU(2) are employed here to analyze the three-roll wrist and the spherical Watt I linkage. Additionally, the five orientation synthesis of a spherical four-bar mechanism is solved, and solutions are found for the eight orientation synthesis of the Watt I linkage. Using SU(2) readily allows for the use of a homotopy-continuation-based solver, in this case Bertini. The use of Bertini is motivated by its capacity to calculate every solution to a design problem.
Research Interests:
Morphometrics is a quantitative analysis to compare a set of geometric representations of forms, including shape and size. Analysis of shape variation is useful in systematics, evolutionary biology, biostratigraphy, and developmental... more
Morphometrics is a quantitative analysis to compare a set of geometric representations of forms, including shape and size. Analysis of shape variation is useful in systematics, evolutionary biology, biostratigraphy, and developmental biology. Distinguished by the data being analyzed, three forms of morphometrics are commonly recognized. Traditional morphometrics measures the lengths, ratios, angles, etc., of patterns of shape variations. Outline-based morphometrics analyzes the outlines of forms using open or closed curves. Landmark-based geometric morphometrics summarizes shapes in terms of the coordinates of anatomical landmarks. The three morphometric methods are able to capture the variation of forms exactly, but require analyzing numerous variables. As an alternative approach to morphometrics, this paper presents a kinematic synthesis methodology of planar rigid-body chains. This methodology approximates the set of profile curves that represent a series of shapes with a single ...
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A spatial analogue of the Stephenson III six-bar mechanism can be formed by the connection of an SPS chain to the coupler of a spherical four-bar linkage. With the prismatic joint actuated, the spherical four-bar is driven via a force... more
A spatial analogue of the Stephenson III six-bar mechanism can be formed by the connection of an SPS chain to the coupler of a spherical four-bar linkage. With the prismatic joint actuated, the spherical four-bar is driven via a force applied directly to the coupler. This linkage is termed the coupler-driven spherical four-bar mechanism, and defines an alternative to the typical scheme of actuating the four-bar via a torque applied at the input link. This paper presents software developed to assist in the kinematic synthesis of these mechanisms. In the first stage of the design, a circuit-defect free spherical four-bar is dimensioned with the capacity to guide a rigid body through two orientations. The second stage of the design is to locate the SPS leg such that the four-bar is smoothly drivable between the orientations.
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Page 1. Proceedings of DETC'05 ASME 2005 Design Engineering Technical Conferences and Computers and Information in Engineering Conference Long Beach, California USA, September 24-28, 2005 DETC05/MECH-84698 ...
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The fixed pivots of a planar 4R linkage that can achieve four design positions are constrained to a center-point curve. The curve is a circular cubic function and plots can take one of five different forms. The center-point curve can be... more
The fixed pivots of a planar 4R linkage that can achieve four design positions are constrained to a center-point curve. The curve is a circular cubic function and plots can take one of five different forms. The center-point curve can be generated with a compatibility linkage obtained from an opposite pole quadrilateral of the four design positions. This paper presents a method to identify design positions that generate distinctive shapes of the center-point curves. The form of the center-point curve is dependent on whether the shape of the opposite pole quadrilateral is an open or closed form of a rhombus, kite, parallelogram, or when the sum of two sides equals the other two. Interesting cases of three and five position synthesis are also explored. Four and five position cases are generated that have center points at infinity allowing a PR dyad with line of slide in any direction to achieve the design positions. Further, a center-point curve for five specific design positions is re...
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ABSTRACT The identification of motion characteristics and assembly circuits is fundamental in creating a workable mechanism. A circuit defect prevents a mechanism from moving between de-sired positions. This paper extends the established... more
ABSTRACT The identification of motion characteristics and assembly circuits is fundamental in creating a workable mechanism. A circuit defect prevents a mechanism from moving between de-sired positions. This paper extends the established methods for analyzing multi-degree-of-freedom platforms to gain insight on single-actuated linkages. Specifically, from a plot of the singu-larity locus projected onto the input joint space, the number of singularities, number of geometric inversions and circuit regimes are revealed. The input/output motion of the linkage can be in-ferred from the locus. The methodology to produce the singu-larity locus is general and does not rely on geometric insights of a particular mechanism. By using the locus, desired operational features can be readily identified, such as a fully rotatable crank. Unique motion characteristics, such as a greater than 360 • non-rotatable crank, can be also be detected. Further, it is observed that transition linkages serve as bounds between the regions of circuit change. 1 INTRODUCTION Forward kinematic position analysis of a mechanism in-volves determining the position and orientation of links as an input link(s) is actuated. Since the governing position equations for the links in a mechanism are non-linear, multiple solutions are obtained for a single position of the input link(s). These differ-ent solutions or various configurations of a mechanism are called geometric inversions (GIs) [1]. For a specific mechanism, the number of GIs is dependent on the position of the input link(s).
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Any articulated system of rigid bodies defines a statically equivalent serial chain (SESC). The SESC is a virtual chain that terminates at the center of mass (CoM) of the original system of bodies. An SESC may be generated experimentally... more
Any articulated system of rigid bodies defines a statically equivalent serial chain (SESC). The SESC is a virtual chain that terminates at the center of mass (CoM) of the original system of bodies. An SESC may be generated experimentally without knowing the mass, CoM, or length of each link in the system given that its joint angles and overall CoM may be measured. This paper presents three developments toward recognizing the SESC as a practical modeling technique. Two of the three developments improve utilizing the technique in practical applications where the arrangement of the joints impacts the derivation of the SESC. The final development provides insight into the number of poses needed to create a usable SESC in the presence of data collection errors. First, modifications to a matrix necessary in computing the SESC are proposed, followed by the experimental validation of SESC modeling. Second, the problem of generating an SESC experimentally when the system of bodies includes a...
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This work presents a comparison between two actuation methods for planar and spherical four-bar mechanisms. The first is actuation by a torque applied at either of the fixed pivots. The second actuation method uses a linear actuator... more
This work presents a comparison between two actuation methods for planar and spherical four-bar mechanisms. The first is actuation by a torque applied at either of the fixed pivots. The second actuation method uses a linear actuator connected between ground and the coupler. For any four position task, planar or spherical, a one parameter set of dyads is found that may be used to guide the body through the four positions. Any two of these dyads, when coupled, define a potential four-bar solution to the task. A sampling across the set of all possible mechanisms that solve the four position task may be compared by analyzing the internal static loads of the four-bar mechanisms. The comparison was conducted to determine if coupler-driven four-bars have reduced internal loading when compared to torque-driven mechanisms. Four position tasks were used for comparison of mechanisms designed for the same task, under the assumption that the optimal torque-driven mechanism would have a different...
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This paper presents a method of selecting joints relative to a fixed and moving (coupler) frame that can be used to actuate a single degree of freedom planar mechanism using a revolute-prismatic-revolute (RPR) chain or a spherical... more
This paper presents a method of selecting joints relative to a fixed and moving (coupler) frame that can be used to actuate a single degree of freedom planar mechanism using a revolute-prismatic-revolute (RPR) chain or a spherical mechanism via a spherical-prismatic-spherical (SPS) chain. Given a single degree of freedom mechanism, a moving reference frame attached to any link has a motion that can be described with a single parameter. A point relative to this moving frame is sought such that it either continually increases or decreases in distance from a point in the fixed frame over the entire motion. The mechanism can then be moved by placing an actuated prismatic joint between the two points. Moreover, the singularities relative to the joints in the original mechanism are not a concern and the dimensional synthesis can focus on creating the set of circuit-defect free solutions. From this analysis, a unique fixed point is determined relative to two positions and their velocities ...
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Given a single degree of freedom mechanism, a moving reference frame attached to any link has a motion that can be described with a single parameter. A point relative to this moving frame is sought such that it either continually... more
Given a single degree of freedom mechanism, a moving reference frame attached to any link has a motion that can be described with a single parameter. A point relative to this moving frame is sought such that it either continually increases or decreases in distance from a point in the fixed frame over the entire motion. These points can be used to define a revolute–prismatic–revolute (RPR) chain for a planar mechanism or a spherical–prismatic–spherical (SPS) chain for a spherical mechanism capable of actuating the device over its entire range of motion. Moreover, the singularities relative to the joints in the original mechanism are not a concern and the dimensional synthesis can focus on creating the set of circuit-defect free solutions. From this analysis, a unique fixed point is determined in the planar case relative to two positions and their velocities with the following characteristic. All points in the moving reference frame that are moving away from it in the first position a...
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A coupler-driver for a planar mechanism is a revolute-prismatic-revolute (RPR) chain connected between ground and one of the links of the mechanism. The focus of this work is to investigate how the use of a coupler-driver as the source of... more
A coupler-driver for a planar mechanism is a revolute-prismatic-revolute (RPR) chain connected between ground and one of the links of the mechanism. The focus of this work is to investigate how the use of a coupler-driver as the source of actuation alters the set of solutions for a four position task by avoiding defects relative to the joints of the actuated mechanism. Type maps are a synthesis tool used to visualize the solutions for the four position task, which previous researchers have used to identify the mechanism class and the ability to actuate each solution through the task. This work extends the type map concept to represent the number of solutions to a four position task that are drivable via either a coupler-driver or an input torque at one of the fixed joints. The use of a coupler-driver as the actuator is found to allow many mechanisms that suffer from a branch defect relative to the joints of the kinematic solution mechanism to be valid solutions. For the example four...
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This paper presents the development of variable geometry dies that enable the extrusion of plastic parts with a varying cross section. Extrusion accounts for 40% of all manufactured plastic parts because it is a relatively low-cost and... more
This paper presents the development of variable geometry dies that enable the extrusion of plastic parts with a varying cross section. Extrusion accounts for 40% of all manufactured plastic parts because it is a relatively low-cost and high-production-rate process. Conventional polymer extrusion technology, however, is limited to fixed dies that produce continuous plastic products of constant cross section defined by the die exit profile. A shape-changing die allows the cross section of the extruded part to change over its length, thereby introducing the capacity to manufacture plastic faster and with lower tooling costs than injection molding. This paper discusses design guidelines that were developed for movable die features including revolute and prismatic joint details, land length, and the management of die leakage. To assess these guidelines, multiple dies have been designed and constructed to include an arbitrary four-sided exit profile where changes were made to the internal...
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... edu Andrew P. Murray Department of Mechanical and Aerospace Engineering University of Daytonandrew. ... rics for determining the distance between two locations of a finite rigid body is still an area of ongoing research, see... more
... edu Andrew P. Murray Department of Mechanical and Aerospace Engineering University of Daytonandrew. ... rics for determining the distance between two locations of a finite rigid body is still an area of ongoing research, see Kazerounian and Rastegar, 1992, Bobrow and Park ...
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ABSTRACT Synthesizing a motion generating 3-jointed planar chain, under no additional constraints, is trivial. Given a set of desired planar rigid body positions, one can select via straightforward geometric considerations the locations... more
ABSTRACT Synthesizing a motion generating 3-jointed planar chain, under no additional constraints, is trivial. Given a set of desired planar rigid body positions, one can select via straightforward geometric considerations the locations of the revolute (R) joints and prismatic (P) joints of a chain that will reach the positions. On the other hand, specifying constraints on joint limitations or physical parameters may result in no chains that reach the desired positions. In this paper, we study a rigid body in a set of positions in order to determine the point on the body that lies nearest a point, circle or line. Note that the point, circle or line is unknown and is determined as part of the process. The set of points formed by the rigid body point in all of its positions defines a workspace for the outermost moving pivot of the chain. By fitting a generic RPR, PRR or RRR chain’s workspace to these points, we can suggest nearly minimal joint constraints and physical parameters.
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One method for generating a Watt II six-bar with a sliding output is to identify the location of its six revolute (R) joints. The location of the output prismatic (P) joint does not need to be identified as it can be assumed to allow... more
One method for generating a Watt II six-bar with a sliding output is to identify the location of its six revolute (R) joints. The location of the output prismatic (P) joint does not need to be identified as it can be assumed to allow vertical motion through the final R joint. If classified, like the 4R, based on the range of motion of each link as cranking or rocking, a number of possibilities exist classifying the four moving links connecting the six R joints. In this paper, we introduce a methodology for ensuring that the link connecting the first two R joints is a crank. As there are four more locations to specify, each location needs to be selected in light of the locations of the previous R joints. To accomplish this goal, we identify the Watt II six-bar transition linkages on the boundary between classifications.