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This paper describes a synthesis technique that constrainsa spatial serial chain into a single degree-of-freedom mechanismusing planar six-bar function generators. The synthesisprocess begins by specifying the target motion of a serialchain that is parameterized by time. The goal is to createa mechanism with a constant velocity rotary input that willachieve that motion. To do this we solve the inverse kinematicsequations to find functions of each serial joint angle withrespect to time. Since a constant velocity input is desired,time is proportional to the angle of the input link, and eachserial joint angle can be expressed as functions of the inputangle. This poses a separate function generator problem tocontrol each joint of the serial chain. Function generatorsare linkages that coordinate their input and output angles.Each function is synthesized using a technique that finds 11position Stephenson II linkages, which are then packagedonto the serial chain. Using pulleys and the scaling capabilitiesof function generating linkages, the final device canbe packaged compactly. We describe this synthesis procedurethrough the design of a biomimetic device for reproducing aflapping wing motion.

Function generation synthesis of mechanisms can be considered as the design of correlation of crank angles and dead dead-center position design. These two problems have been clearly defined and solved separately. But some problems may require both correlation of crank angles and dead dead-center design at different configurations. Such problems are called mixed function generation problems. In this paper, an overview of these mixed function generation problems for the planar four-bar mechanism are given and the problems are solved analytically or semi-analytically. Except three of them, all presented mixed function generation problem formulations are novel. The solutions of all problems including three positions for the four-bar mechanism and the solution of a problem including four positions for a four-bar mechanism are addressed. All problems are first reduced to a univariate equation and a fast solution is found. Thus, link lengths can be found quickly by changing the problem definition problems, and several design iterations can be performed in a short time. Numerical solutions of all problems have been demonstrated using Excel. [ABSTRACT FROM AUTHOR]

Four-bar linkages are critical fundamental elements of many mechanical systems, and their design synthesis is often mathematically complicated with iterative numerical solutions. Analytical methods based on Fourier coefficients can circumvent these difficulties but have issues with time parameters assignment for path generation without prescribed time in previous studies. In this paper, an improved Fourier-based point-to-point combination method is presented, which generates more points by Fourier approximation and assigns the time parameters to the given points while allowing discarding solutions with order defects. This method relies on the Fourier coefficients, improving the accuracy of synthesis solutions, and simplifying the computational procedure. Time parameters are assigned directly to the given points, which avoids the complex calculations to find intersection points in the given path, eliminates combinations that would lead to solutions with order defects, and simplifies the assessment process of synthesis results. The parameters obtained by the point-to-point combination method can be used as the parameters of the input dyad, skipping the first set of design equations for faster calculation. Several examples are presented to demonstrate the advantages of the proposed synthesis method, which is easy-understanding, computationally efficient, and yields more accurate solutions than available synthesis methods. [ABSTRACT FROM AUTHOR]

AbstractRobotic Hand Grasping is a challenging task that is studied by different researchers, with contributions made to topics such as grasping quality measuring, synthesis, and mathematical models. However, these works usually consider grasping of only one object at time, which is not applicable when the hand must carry multiple objects. Multiple objects grasping problem can be approached as a packing problem, which consists in filling a container with objects of a determined geometry, using the space available in the most efficient way. The aim of this work is to obtain a design methodology for a two-finger gripper that optimizes the grasping capacity of slender cylindrical multiple objects, applying packing problem concepts. This case is of practical importance in grapple claws used in forest harvesting for picking logs. A mathematical model is presented that allows to obtain an optimized geometric configuration of the grapple claw for maximum grasping capacity and packing density for given numbers and sizes of logs. This model is analytically solved for the maximum radius of a set of logs that can be grasped. Alternatively, for a number of logs with a given diameter, the geometric dimensions of an optimized grapple claw can be obtained. The solutions are evaluated using packing density and Active Force Closure (AFC) as quality metrics, to show the benefits of adding them as design criteria in the design multiple objects grapple claws. [ABSTRACT FROM AUTHOR]

Gears are foundational tools used to transmit or modify mechanical energy or motion. Implementing gears into planar linkage mechanisms is less common but can be a similarly valuable technique that takes advantage of the high efficiency of gears while producing complex and precise motions. While recent numerical methods for designing these geared planar linkage mechanisms (GPLMs) have proliferated in the literature, analytical approaches have their merits and have received less attention. Here, an analytical alternative is presented as a modification of the complex-number loop-based synthesis method for designing multiloop mechanisms. Some of the base topologies for geared dyad, triad, and quadriad chains are presented, along with a numerical example demonstrating the solution procedure's effectiveness. [ABSTRACT FROM AUTHOR]

To achieve the precise operation trajectory and posture required for pot seedling transplanting and solve the problem that the partial reversal of the transplanting arm's output in the double planet carrier transplanting mechanism, which is unconducive to the realization of the seedling pushing action, a motion synthesis method for a double planet carrier gear train mechanism with attitude constraints based on the output angle and four exact task poses is proposed. First, the ideal transplanting trajectory is planned according to the transplanting agronomic requirements, and the position and attitude information of the four key points on the ideal trajectory are extracted as the constraints of the mechanism design. Then, based on the relative displacement equation, a comprehensive design equation of the motion of the plane 3R mechanism (simplified model of the transplanting mechanism) about the output rotation angle and the precise four pose constraints is established, and the mechanism parameters that meet the constraint requirements are obtained by solving the multicellular homotopy method. A mathematical model of the roundness of the non-circular gear was also established, and the roundness of the transmission non-circular gears in the gear-train transplanting mechanism was optimized by using the genetic algorithm. Finally, the structural design, virtual simulation, and experimental analysis of the double-planet carrier gear train transplanting mechanism were completed. The results show that the actual trajectory and attitude are consistent with the theoretical design, and when then the mechanism was under the transplanting efficiency of 120 and 180 plants/min, the success rates of picking seedlings were 91.53% and 87.46%, respectively, meeting the design requirements. [ABSTRACT FROM AUTHOR]

Developable mechanisms provide unparalleled compactness and deployability. This paper explores the kinematic behavior of developable mechanisms that conform to regular cylindrical surfaces. Design considerations that aid in the dimensional synthesis of these mechanisms are developed and demonstrated through case studies. The design implications, limitations, and opportunities associated with regular cylindrical developable mechanisms are discussed through the lens of both an analytical and graphical methods. [ABSTRACT FROM AUTHOR]

Four-bar linkages are critical fundamental elements of many mechanical systems, and their design synthesis is often mathematically complicated with iterative numerical solutions. Analytical methods based on Fourier coefficients can circumvent these difficulties but have issues with time parameters assignment for path generation without prescribed time in previous studies. In this paper, an improved Fourier-based point-to-point combination method is presented, which generates more points by Fourier approximation and assigns the time parameters to the given points while allowing discarding solutions with order defects. This method relies on the Fourier coefficients, improving the accuracy of synthesis solutions, and simplifying the computational procedure. Time parameters are assigned directly to the given points, which avoids the complex calculations to find intersection points in the given path, eliminates combinations that would lead to solutions with order defects, and simplifies the assessment process of synthesis results. The parameters obtained by the point-to-point combination method can be used as the parameters of the input dyad, skipping the first set of design equations for faster calculation. Several examples are presented to demonstrate the advantages of the proposed synthesis method, which is easy-understanding, computationally efficient, and yields more accurate solutions than available synthesis methods.

Planar mechanisms are essential for many applications. The metal forming process is a vital application for industrial sectors such as automotive and space. Manufacturing precision and generating dwell motion are also important issues. These properties cannot be realized on conventional mechanical presses. Therefore, a novel single degree of freedom (1DOF) eight-bar planar mechanism was developed in this study. The main advantages of the new mechanism are slider balance and dwell motion without a servo motor. Thanks to these advantages, manufacturing difficulty and cost can be reduced. In this study, the new mechanism was modeled kinematically and verified. An optimization methodology was also presented for determining the mechanism dimensions. In order to achieve the desired dwell motion, dimensions of the mechanism for three cases (stroke capacities with 60 mm, 600 mm (crank length ≤ 300 mm), and 600 mm (crank length ≤ 250 mm)) were optimized by using the Genetic Algorithm (GA). The optimized dimensions were also compared kinematically, and the comparison results were shown. The best-optimized dimensions were determined based on the position, velocity, and acceleration simulations of the new mechanism. [ABSTRACT FROM AUTHOR]

This paper presents the new synthesis models of spatial linkages for designing measurement motion functions and ranges and identifying the actual dimension parameters. The spatial five-bar linkage is first introduced for the kinematic model of a double ball bar test of a two-axis rotary table. To design the ideal measurement motion and motion range of the double ball bar test, a novel saddle synthesis model of a spatial four-bar linkage RRSS is readily presented. Based on the output data measured from the double ball bar test, a new saddle synthesis model of a spatial five-bar linkage RRSPS is logically proposed for identifying their actual dimensions. Finally, three test cases and their results indicate that the new synthesis models presented in the paper can conveniently and efficiently calculate the measurement motion function and range and accurately identify the actual dimensions of the double ball bar test, which provides a suitable mathematical model for improving the accuracy of the double ball bar tests of a two-axis rotary table of machine tools. [ABSTRACT FROM AUTHOR]

The MK circles represent a kinematic synthesis tool for the dimensional synthesis of planar dyads. The tool is uniquely useful in its ability to both find specific dyad solutions and help the designer visualize numerous potential dyad pivot locations in the solution space. Here, the existing understanding of MK circles is summarized for three and four specified motion positions and extended for additional positions. Then the technique is expanded to show its application to MKT circles for triad synthesis, including solution space visualization, ground pivot specification, and multi-loop synthesis of complex mechanisms. These methods are illustrated by a unifying example that provides a sample procedure for applying the MK/MKT circles, and implements each of the aforementioned techniques. The interchangeability of loop-based synthesis approaches is demonstrated by comparing the new methodology to the compatibility linkages technique. [ABSTRACT FROM AUTHOR]

This paper describes a synthesis technique that constrainsa spatial serial chain into a single degree-of-freedom mechanismusing planar six-bar function generators. The synthesisprocess begins by specifying the target motion of a serialchain that is parameterized by time. The goal is to createa mechanism with a constant velocity rotary input that willachieve that motion. To do this we solve the inverse kinematicsequations to find functions of each serial joint angle withrespect to time. Since a constant velocity input is desired,time is proportional to the angle of the input link, and eachserial joint angle can be expressed as functions of the inputangle. This poses a separate function generator problem tocontrol each joint of the serial chain. Function generatorsare linkages that coordinate their input and output angles.Each function is synthesized using a technique that finds 11position Stephenson II linkages, which are then packagedonto the serial chain. Using pulleys and the scaling capabilitiesof function generating linkages, the final device canbe packaged compactly. We describe this synthesis procedurethrough the design of a biomimetic device for reproducing aflapping wing motion.

The conventional approach of the mechanism design process, generally, has a two-step procedure: Kinematic synthesis/analysis of the mechanism in the first step and optimization of the synthesized/analyzed mechanism based on optimization criteria in the second step. This study presents an approach that combines kinematic synthesis with the static balancing of the same, and optimization, into a one-step procedure. As an example of this one-step design process, a tension-spring assisted four-bar hood linkage optimal synthesis and design is performed in one-step. This one-step solution includes kinematic synthesis and analysis of the hood linkage, virtual work, static balancing with tension spring, and optimization in the presence of joint friction. The resulting design requires a minimum force to raise and lower the hood in the presence of unknown optimum levels of joint friction while the hood is statically balanced for its entire range of motion. A total of twelve different scenarios are investigated and the results are discussed.

Gears are foundational tools used to transmit or modify mechanical energy or motion. Implementing gears into planar linkage mechanisms is less common but can be a similarly valuable technique that takes advantage of the high efficiency of gears while producing complex and precise motions. While recent numerical methods for designing these geared planar linkage mechanisms (GPLMs) have proliferated in the literature, analytical approaches have their merits and have received less attention. Here, an analytical alternative is presented as a modification of the complex-number loop-based synthesis method for designing multiloop mechanisms. Some of the base topologies for geared dyad, triad, and quadriad chains are presented, along with a numerical example demonstrating the solution procedure’s effectiveness.

The design of a flapping fins stabilization system for yachts at anchor (zero speed conditions) is presented in this study. The solution presented in this manuscript took inspiration from a solution proposed for the design of a biologically inspired flapping UAV. Although the application was different, we used the same principles and methodology to design and study the stabilization mechanism discussed hereafter. The proposed system uses flapping fins to damp the roll oscillations of the vessel, and when the stabilization system is retracted, the surface of each of the fins is flush with the hull, thus offering minimum resistance when the ship is in cruise conditions. The unsteady forces of the flapping fins were computed using computational fluid dynamics, and they were used as input to conduct the structural and durability study of the proposed mechanism. The vessel's response to roll perturbations was also studied, using a multi-body dynamics approach. From the results obtained, and the design specifications defined, it was found that the response of the stabilization system was acceptable, and that the mechanism could withstand the inertial and hydrodynamic loads. [ABSTRACT FROM AUTHOR]

To obtain a picking and planting integrated transplanting mechanism (PITM) with ideal trajectory shape, reasonable operating attitude, and compact structure for vegetable pot seedling transplanting, a symmetrical structural PITM composed of two planetary carriers and driven by a cam–noncircular gear combination mechanism was proposed in this paper. In accordance with the requirements of transplanting agronomy, the shape of the motion trajectory and the attitude of the end tip of the clamping claw at several specific positions (the starting and end points of picking seedling, the starting point of pushing seedling, and a special point on the return segment) were planned. To make the clamping claws of PITM pass through a set of prescribed positions, the mechanism was simplified to an open-chain 3R mechanism. An accurate four-position-based method for solving the open-chain mechanism model was adopted to obtain the curves of its fixed hinge point (central point) and dynamic hinge point (circle point). The ratio of adjacent bars’ lengths was analyzed to determine the feasible interval of the central and circle point curves and the reasonable link length. A desired closed transplanting trajectory that goes through the given points and the corresponding transmission ratio model of the open-chain mechanism was established. After the transmission ratio of each stage of gear and cam pairs was calculated and distributed, the prototype of PITM was designed and manufactured. Lastly, the effectiveness and feasibility of the design were verified through a preliminary experiment of the prototype. [ABSTRACT FROM AUTHOR]

A new family of iterative methods with a strong converging order of twenty to solve nonlinear equations and systems is presented in this study. A simple strategy of blending some existing methods is used to develop the proposed family. The theoretical order of convergence is derived by employing Taylor's series. The performance of the iterative methods in the proposed family is examined by applying the methods on real-world engineering problems. A nonlinear equation modeled by NASA for launching "Wind" satellite and some other complex applied systems, such as combustion problem, tank-reactor problem, kinematic synthesis mechanism, neurophysiology application and one boundary-value problem, have been solved to check the performance of the proposed family against other methods under similar test conditions. All the numerical results show that the proposed family converges very fast in complex and difficult problems as compared to other well-known methods. The methods in the proposed family have an efficiency improvement of 11.99% over the classical Newton method for scalar nonlinear equations. [ABSTRACT FROM AUTHOR]

In Minimally Invasive Surgery (MIS) surgeons operate through small incisions in the body of the patient and due to the lack of the degrees of freedom their capability to manipulate the organs is limited. Thus, surgeons are forced to adopt awkward postures and this may lead to musculoskeletal injuries. This paper presents a new articulated mechanism designed for application in MIS providing an additional degree of freedom in the instrument. The new degree of freedom makes possible the rotation of the end-effector from 0° to 90° and enhances the dexterity of the tool. In this way, the capability to reach the organs is improved and the surgeon reduces the forced motion of hand, wrist and arm. The paper also presents the design process including the synthesis procedure with 2-dof linkage, which is an original contribution of this work. A prototype of the tool is shown at the end of the paper. [ABSTRACT FROM AUTHOR]

In this paper, the compact reducer which can be used as a rigid drive mechanism with a high-speed reduction ratio is systematically studied for kinematics and dynamics. The speed ratio is determined by the number of cam lobes and engaged rollers. The eccentric rotating conjugate lobe cam profile is synthesized by using the rigid body transformation method. To characterize the input torque based on Newton's second law, the transmission forces of the resisting and driven multi-roller are proportional to the arm length of each actuating roller found by its geometric vector. In consideration of machining undercutting, roller limit load, and contact stresses, favorable designs can be achieved by adjusting the cam size, turret dimension, eccentricity, and roller size. Together with experimental tests, a prototype of the lobe cam reducer is made to verify the feasibility of the proposed design procedure and to investigate its kinematic and dynamic characteristics for speed reduction ratios, torques, and transmission efficiency. [ABSTRACT FROM AUTHOR]

Following the COVID-19 outbreak, the redesign of an emergency mechanical pulmonary ventilator that is cheap and easily portable became necessary in several contexts, such as emergency hotspots and environments with poor resources. To address this important issue, a general multibody approach is employed in this paper to develop a reciprocating mechanism suitable for retrofitting the existing manual mechanical ventilators through computer-aided engineering tools. By analyzing various basic articulated mechanisms typically found in engineering mechanics, a prototype is created and reproduced in a three-dimensional environment using SOLIDWORKS's CAD software. Subsequently, a high-fidelity mechanical model is developed starting from the CAD geometry and employing the SIMSCAPE MULTIBODY software, an extension of the MATLAB family of programs that can effectively and efficiently perform kinematic and dynamic simulations of the mechanism of interest. As discussed in the paper, by carrying out numerous numerical experiments, the virtual simulations predict several fundamental medical parameters, such as the airflow introduced into patients, the respiratory rate, and the respiratory ratio.

This paper presents the new synthesis models of spatial linkages for designing measurement motion functions and ranges and identifying the actual dimension parameters. The spatial five-bar linkage is first introduced for the kinematic model of a double ball bar test of a two-axis rotary table. To design the ideal measurement motion and motion range of the double ball bar test, a novel saddle synthesis model of a spatial four-bar linkage RRSS is readily presented. Based on the output data measured from the double ball bar test, a new saddle synthesis model of a spatial five-bar linkage RRSPS is logically proposed for identifying their actual dimensions. Finally, three test cases and their results indicate that the new synthesis models presented in the paper can conveniently and efficiently calculate the measurement motion function and range and accurately identify the actual dimensions of the double ball bar test, which provides a suitable mathematical model for improving the accuracy of the double ball bar tests of a two-axis rotary table of machine tools.

The MK circles represent a kinematic synthesis tool for the dimensional synthesis of planar dyads. The tool is uniquely useful in its ability to both find specific dyad solutions and help the designer visualize numerous potential dyad pivot locations in the solution space. Here, the existing understanding of MK circles is summarized for three and four specified motion positions and extended for additional positions. Then the technique is expanded to show its application to MKT circles for triad synthesis, including solution space visualization, ground pivot specification, and multi-loop synthesis of complex mechanisms. These methods are illustrated by a unifying example that provides a sample procedure for applying the MK/MKT circles, and implements each of the aforementioned techniques. The interchangeability of loop-based synthesis approaches is demonstrated by comparing the new methodology to the compatibility linkages technique.

The design of a flapping fins stabilization system for yachts at anchor (zero speed conditions) is presented in this study. The solution presented in this manuscript took inspiration from a solution proposed for the design of a biologically inspired flapping UAV. Although the application was different, we used the same principles and methodology to design and study the stabilization mechanism discussed hereafter. The proposed system uses flapping fins to damp the roll oscillations of the vessel, and when the stabilization system is retracted, the surface of each of the fins is flush with the hull, thus offering minimum resistance when the ship is in cruise conditions. The unsteady forces of the flapping fins were computed using computational fluid dynamics, and they were used as input to conduct the structural and durability study of the proposed mechanism. The vessel’s response to roll perturbations was also studied, using a multi-body dynamics approach. From the results obtained, and the design specifications defined, it was found that the response of the stabilization system was acceptable, and that the mechanism could withstand the inertial and hydrodynamic loads.

This paper presents a synthesis method for the Stephenson III six-bar linkage that combines the direct solution of the synthesis equations with an optimization strategy to achieve increased performance for path generation. The path synthesis equations for a six-bar linkage can reach as many as 15 points on a curve; however, the degree of the polynomial system is 1046. In order to increase the number of accuracy points and decrease the complexity of the synthesis equations, a new formulation is used that combines 11 point synthesis with optimization techniques to obtain a six-bar linkage that minimizes the distance to 60 accuracy points. This homotopy directed optimization technique is demonstrated by obtaining a Stephenson III six-bar linkage that achieves a specified gait trajectory.

This paper presents a design system for planar eight-bar linkages that begins with a user specified 6R planar loop and five required configurations, and computes two RR constraints that yield an eight-bar linkage. There are 32 ways that these constraints can be added to the 6R loop to yield as many as 340 different linkages, which include eight of the 16 eight-bar linkage topologies. An analysis routine based on the Dixon determinant is used to verify the performance of each design candidate. Random variation of task configurations within user specified tolerance zones is used to increase the number of candidate designs. The result is an effective system for the design of eight-bar linkages, which is demonstrated by designing linkages that guide movement though a symmetric and offset set of parallel task positions along a straight line.

This paper describes a synthesis technique that constrains a spatial serial chain into a single degree-of-freedom mechanism using planar six-bar function generators. The synthesis process begins by specifying the target motion of a serial chain that is parameterized by time. The goal is to create a mechanism with a constant velocity rotary input that will achieve that motion. To do this, we solve the inverse kinematics equations to find functions of each serial joint angle with respect to time. Since a constant velocity input is desired, time is proportional to the angle of the input link, and each serial joint angle can be expressed as functions of the input angle. This poses a separate function generator problem to control each joint of the serial chain. Function generators are linkages that coordinate their input and output angles. Each function is synthesized using a technique that finds 11 position Stephenson II linkages, which are then packaged onto the serial chain. Using pulleys and the scaling capabilities of function generating linkages, the final device can be packaged compactly. We describe this synthesis procedure through the design of a biomimetic device for reproducing a flapping wing motion.

The approximate path synthesis of four-bar linkages has been framed and solved with many different optimization techniques. Here we present a polynomial objective that is invariant to the number of approximate design positions selected, and a solution technique capable of finding all minima. The invariance property caps compute time despite increasing the size of input task specification data. This is performed by collecting a variable amount of task data into an invariable number of polynomial coefficients, called moments , before numerical optimization begins. The minima are found by applying the method of random monodromy loops to the zero gradient polynomial system of the aforementioned objective. This procedure finds all critical points, including the local and global minimum, and provides an in-process estimate of the percentage of critical points found. We applied our methodology to four-bar path synthesis problems of various computational scales by altering dimensional pre-specifications. The most general case was estimated to have 1,820,238 ± 3810 critical points, while pre-specification of one or two ground pivots yielded 26,052 and 503 roots, respectively, as validated by a trace test. The results are applied to a variety of examples. [Display omitted] • The approximate kinematic synthesis of four-bar linkages is solved in near completeness. • Random monodromy loops solve the polynomial objective for an optimization landscape. • Generic total system solve results in 1,820,238 ± 3810 critical points. • Generic solution sets are used as starting point for parameter homotopies with examples provided. [ABSTRACT FROM AUTHOR]

This paper presents a direct solution of the kinematic synthesis equations for Stephenson III six-bar function generators to achieve as many as 11 accuracy points. The approach is similar to that used to design Stephenson II function generators, except additional algebraic manipulations reduce the system to a multihomogeneous degree of 55,050,240. A numerically general multihomogeneous homotopy was used to obtain 834,441 nonsingular solutions, which were then used to construct an efficient parameter homotopy for specific tasks consisting of 11 accuracy points. The thousands of linkage solutions found by this parameter homotopy are sorted and analyzed to verify nonbranching movement through the specified task positions. An example is presented of a function generator that creates a specified torque-angle profile for a dynamic wrist splint that cancels the effects of spasticity in the wrists of stroke survivors.

This paper presents a direct solution of the kinematic synthesis equations for Stephenson III six-bar function generators to achieve as many as 11 accuracy points. The approach is similar to that used to design Stephenson II function generators, except additional algebraic manipulations reduce the system to a multihomogeneous degree of 55,050,240. A numerically general multihomogeneous homotopy was used to obtain 834,441 nonsingular solutions, which were then used to construct an efficient parameter homotopy for specific tasks consisting of 11 accuracy points. The thousands of linkage solutions found by this parameter homotopy are sorted and analyzed to verify nonbranching movement through the specified task positions. An example is presented of a function generator that creates a specified torque-angle profile for a dynamic wrist splint that cancels the effects of spasticity in the wrists of stroke survivors.

This paper presents a design methodology for Stephenson II six-bar function generators that coordinate 11 input and output angles. A complex number formulation of the loop equations yields 70 quadratic equations in 70 unknowns, which is reduced to a system of ten eighth degree polynomial equations of total degree 810 = 1:07 × 109. These equations have a monomial structure which yields a multihomogeneous degree of 264,241,152. A sequence of polynomial homotopies was used to solve these equations and obtain 1,521,037 nonsingular solutions. Contained in these solutions are linkage design candidates which are evaluated to identify cognates, and then analyzed to determine their input-output angles in each assembly. The result is a set of feasible linkage designs that reach the required accuracy points in a single assembly. As an example, three Stephenson II function generators are designed, which provide the input-output functions for the hip, knee, and ankle of a humanoid walking gait.

This paper presents a design system for planar eight-bar linkages that adds three RR constraints to a user-specified 4R serial chain. R denotes a revolute, or hinged, joint. There are 100 ways in which these constraints can be added to yield as many as 3951 different linkages. An analysis routine based on the Dixon determinant evaluates the performance of each linkage candidate and determines the feasible designs that reach the task positions in a single assembly. A random search within the user-specified tolerance zones around the task specifications is iterated in order to increase the number of linkage candidates and feasible designs. The methodology is demonstrated with the design of rectilinear eight-bar linkages that guide an end-effector through five parallel positions along a straight line.

The standard recovery treatment for ankle and lower leg injuries consists of using underarm crutches. Hands-free crutches have recently emerged as a more comfortable, natural and energy efficient alternative. However in the currently available devices such as the iWalk-Free (iWALKFree, Inc., USA) the lack of a knee joint results in abnormal motion pattern at the hip and pelvic joints to ensure foot clearance during the swing phase of the gait. To address this shortcoming, the paper describes the kinematic synthesis of a planar passive four-bar linkage that can be used as a mechanical knee in lower limb exoskeletons and other wearable devices. The knee design is based on anthropomorphic foot walking trajectory obtained from optical motion capture system. The task geometry at the foot, related to the contact and curvature constraints between the foot and the ground at two critical positions 'heel strike' and 'toe off' is scaled to the knee level. Velocity and acceleration specifications compatible with the contact and curvature constraints assist in defining the synthesis equations for the knee design. A working prototype of a passive wearable crutch substitute that incorporates the mechanical knee shows the applicability of the proposed technique.

This paper explores an automated methodology to design eight-bar linkages for five positions, by constraining the user defined 4R open chain and 6R closed chain using RR dyads. The application in focus is that of rectilinear motion. The paper lays down the rules for systematic selection of link pairs for the application of RR constraints, that help automate the synthesis of eight-bar linkages. The methodology performs a random search within the user specified tolerance zones around the task specifications to increase the number of candidate linkage solutions. These linkages are then subjected to forward kinematic analysis using the Dixon determinant elimination procedure to find all possible linkage configurations over the range of motion of the input link. Linkages that have all the task configurations on one branch ensure their smooth movement through them. The result is an array of defect-free eight-bars that can perform approximate rectilinear motion. This method provides increased flexibility and control over the synthesized linkage compared to other known rectilinear motion linkages, owing to the ability to specify the backbone chain. A couple of examples are presented to illustrate the results.