J. Michael McCarthy

• PhD
• Professor (Full) at University of California, Irvine

This paper presents an unmanned surface vehicle (USV) powered by oars configured with a set of three oars on the port and starboard sides. Spherical four-bar links support each of the oars and are designed to guide the oar blade through a rowing movement around a virtual center of a sphere located at the base of the linkage. The input cranks of the...

This article describes a robot walker based on a new single degree-of-freedom six-bar leg mechanism that provides rectilinear, non-rotating, movement of the foot. The walker is statically stable and requires only two actuators, one for each side, to provide effective walking movement on a flat surface. We use Curvature Theory to design a four-bar l...

The trajectory tracking control of 3-RPS parallel mechanisms which severs to motion control is widely used in industrial, medical, aerospace and other fields. However, the existing method are troubled by complicated calculation of Lagrange multipliers. To address this problem, we propose a new method for trajectory tracking control of 3-RPS paralle...

This paper presents a design study for a novel modular robot walker formed from a series of modules having two lateral leg mechanisms, each with only one degree-of-freedom. The lateral leg mechanism is constructed from two six-bar linkages joined, \(180^\circ \) out-of-phase, to one input crank and driven by one stepper motor. This design study sho...

This paper presents recent research in the design of continuous structures that deflect to achieve a specified movement. The procedure starts with a graph that describes the structure as vertices and edges with a designated workpiece, i.e. a platform whose movement is of interest. The size and shape of these graph elements are transformed and the a...

This paper presents research on the fabrication of a continuum mechanism designed to match the movement of a folding linkage. A continuum mechanism is a single part that is designed to deflect in a prescribed manner. This paper presents the result of the fabrication of parts intended to reproduce the folding movement of a six-bar linkage. A combina...

In this paper, we present the design of a pneumatically actuated skeleton for a robotic fish. The tail is designed as a one degree of freedom coiling truss that is actuated by air pressure supplied to pouch actuators along the truss. We present that kinematic synthesis procedure, the fabrication and testing of the fish tail system. Our goal is an e...

This paper modifies Jansen’s leg mechanism so that it is formed by an RR serial chain with hip and knee joints driven by separate four-bar function generators with one input. Kinematic synthesis of the two function generators programs the joint movement of the RR leg to achieve a desired foot trajectory. The two input cranks can be connected by gea...

This paper presents an implementation of a homotopy path tracking algorithm for polynomial numerical continuation on a graphical processing unit (GPU). The goal of this algorithm is to track homotopy curves from known roots to the unknown roots of a target polynomial system. The path tracker solves a set of ordinary differential equations to predic...

This paper presents the design of planar trusses constructed from a sequence of four-bar linkages that guide a one degree-of-freedom coiling movement of the truss from a linear deployed configuration to a coiled circular or coiled spiral stowed configuration. For a given number of modules in the truss, the dimensions of each module are identical fo...

Forceps are a multifunctional tool that can solve various grasping needs. An action origami-based forcep design allows a structure to deploy from a flat state to 3D state plus create motion while in a final 3D state. The origami-based design allows the structure to compact. A fabric inflatable structure allows for shape transformation and stiffness...

This paper presents a design methodology for mechanisms consisting of a single continuous structure, continuum mechanisms, that blends the kinematic synthesis of rigid-body mechanisms with topology optimization for compliant mechanisms. Rather than start with a generic structure that is shaped to achieve a required force deflection task for a compl...

A developable mechanism is a linkage that has its axes located on a developable ruled surface and its links shaped to fit this surface in a stowed configuration. Our goal is to find a configuration of a four-bar linkage in which a circle passes through the four joint axes. This configuration can form the stowed position of the linkage with its link...

This paper presents an implementation of a path tracking algorithm and end game for the homotopy solution of mechanism synthesis equations using a graphical processing unit, or GPU. The goal is to have the GPU execute a large number of path tracking solutions in parallel in order to identify design candidates that satisfy a set of kinematic synthes...

This paper presents a new two-step design procedure and preliminary kinematic evaluation of a novel, passive, six-bar knee-ankle-foot orthosis (KAFO). The kinematic design and preliminary gait analysis of the KAFO are based on motion capture data from a healthy male subject. Preliminary kinematic evaluation shows that the designed passive KAFO is c...

This volume gathers the latest fundamental research contributions, innovations, and applications in the field of design and analysis of complex robotic mechanical systems, machines, and mechanisms, as presented by leading international researchers at the 1st USCToMM Symposium on Mechanical Systems and Robotics (USCToMM MSR 2020), held in Rapid City...

This paper presents a method to develop continuum/compliant mechanisms based on planar bar-node linkage precursors. The method takes as inputs the initial node positions and connectivity data of a given bar-node linkage and converts it into a continuum/compliant mechanism having the same targeted motion. The line bars of the given bar-node linkage...

In the design of practical grasping tools such as forceps or grippers, it may be desirable to create a compact, lightweight, and easily manufactured tool. Origami inspired designs can help simplify gripper manufacturing to a single planar sheet of material while still allowing for deployment and actuation. Inflatable structures can reduce weight an...

This paper examines the results of synthesis algorithms for four-, six-, and eight-bar linkages for rectilinear movement. Rectilinear movement is useful for applications such as suspensions that provide linear movement with out a rotation component. The algorithm yields one four-bar, seven six-bar, and 32 eight-bar linkages. The synthesis strategy...

This paper presents a tutorial on the formulation and solution of the five position synthesis equations for a four-bar linkage in a way that is convenient for implementation using polynomial homotopy software. Complex numbers are used to formulate the loop equations for the four-bar linkage with a coupler reference frame in each of five task positi...

The kinematic synthesis of six-bar linkages involves the solution of polynomial design equations that can have a total degree in the billions and thus requires polynomial homotopy continuation to find solutions. Here we present a six-linkage design system integrated with a parallel implementation of the polynomial homotopy solver Bertini that provi...

The paper presents the development of a customizable lower-leg orthotic device. It consists of a single degree of freedom multi-loop linkage designed to facilitate task-specific lower extremity training for rehabilitation purposes. The device guides the knee, ankle and foot of the user along a walking trajectory obtained from motion capture of a he...

This paper applies kinematic synthesis theory to obtain the dimensions of a constrained spatial serial chain for a valve mechanism that cleans and closes a soil conditioning port in a tunnel boring machine. The goal is a smooth movement that rotates a cylindrical array of studs into position and then translates it forward to clean and close the por...

This paper presents a design procedure to achieve a flapping wing mechanism for a micro-air vehicle that coordinates both the wing swing and wing pitch with one actuator. The mechanism combines a planar four-bar linkage with a spatial four-bar linkage attached to the input and output links forming a six-bar linkage. The planar four-bar linkage was...

Kempe’s universality theorem introduced in 1876 has recently been proven to ensure that given any algebraic curve a mechanism exists that traces the curve. In this paper, we present two methods to simplify Kempe’s linkages. One method uses gear trains, differentials and belt drives to replace his multiplicator, additor and translator linkages. A se...

This paper designs a one degree-of-freedom (1DOF) spatial flapping wing mechanism for a hovering micro-air vehicle by constraining a spatial RRR serial chain using two SS dyads. The desired wing movement defines the dimensions and joint trajectories of the RRR spatial chain. Seven configurations of the chain are selected to define seven precision p...

This paper presents a design procedure to achieve a flapping wing mechanism for a micro air vehicle that drives both the swing and pitch movement of the wing with one actuator. The mechanism combines a planar four bar linkage with a spatial RSSR attached to the input and output links forming a spatial Stephenson six-bar linkage. Function generation...

This paper presents a design and manufacturing methodology for a mechanical system that draws trigonometric curves assembled from a series of links connected by gears. We demonstrate this technique using 11 gear-coupled links that trace a butterfly curve. The equation of a butterfly curve is converted to the relative rotations of the links of a cou...

The paper presents the design of a lower leg orthotic device based on dimensional synthesis of multi-loop six-bar linkages. The wearable device is comprised of a 2R serial chain, termed the backbone, sized according to the wearer’s limb anthropometric dimensions. The paper is a result of our current efforts in proposing a systematic process for the...

This paper presents a design methodology for a system of linkages that can trace planar Bezier curves that represent cursive handwriting of the alphabet and Chinese characters. This paper shows that the standard degree n Bezier curve can be reparameterized so that it takes the form of a trigonometric curve that can be drawn by a one degree-of-freed...

This paper presents a synthesis methodology for a planar linkage that draws a given plane algebraic curve. The existence of such a linkage was demonstrated by A. B. Kempe, who used by specialized linkages, known as additor, mutiplicator and translator linkages, to constrain the two joints of a planar two-link serial chain so that its end point trac...

This paper describes a mechanism design methodology that draws plane curves which have finite Fourier series parameterizations, known as trigonometric curves. We present three ways to use the coefficients of this parameterization to construct a mechanical system that draws the curve. One uses Scotch yoke mechanisms for each of the terms in the coor...

A cycle basis in an undirected graph is a minimal set of simple cycles whose symmetric differences include all Eulerian subgraphs of the given graph. We define a rooted cycle basis to be a cycle basis in which all cycles contain a specified root edge, and we investigate the algorithmic problem of constructing rooted cycle bases. We show that a give...

In this paper we examine two spherical parallel manipulators constructed with legs that include planar and spherical sub-chains that combine to impose constraints equivalent to hidden revolute joints. The first has supporting serial chain legs constructed from three revolute joints with parallel axes, denoted RkRkR, followed by two revolute joints...

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...

This paper describes a mechanism design methodology that assembles standard components to trace plane curves that have a Fourier series parameterization. This approach can be used to approximate complex plane curves to interpolate image boundaries constructed from points. We describe three ways to construct a mechanism that generates a curve from a...

In this paper, we study the manifold of configurations of a 3SPS-1S spherical parallel manipulator. This manifold is obtained as the intersection of quadrics in the hypersphere defined by quaternion coordinates and is called its constraint manifold. We then formulate Jacobian for this manipulator and consider its singular. This is a quartic algebra...

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 polyno...

This paper presents a linkage system designed to guide a natural ankle trajectory with the corresponding foot orientation. A six-bar linkage was designed to coordinate the joint angles of an RR chain (R denotes a revolute or hinged joint) that models the leg to achieve the desired ankle trajectory. The design is shown to be adjustable to meet a ran...

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....

This paper presents a design procedure for Stephenson I-III six-bar linkages that guide a point along a specified trajectory. The first step is to identify an RR serial chain with a point on its end-link that traces the required trajectory. Eleven configurations of this chain are selected to provide accuracy points for the synthesis of Stephenson I...

This chapter focuses on the principles that guide the design and construction of robotic systems. The kinematics equations and Jacobian of the robot characterize its range of motion and mechanical advantage, and guide the selection of its size and joint arrangement. The tasks a robot is to perform and the associated precision of its movement determ...

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 th...

In this paper, we introduce a method to design useful four-bar and six-bar linkages that reach more than the five specified task positions used in Burmester synthesis of RR cranks. Similar to existing methods, we minimize the crank-length error in each task position, however our approach does not introduce penalty functions to eliminate defective l...

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 th...

This paper replaces the hinged pivots of an eight-bar linkage with flexure joints in order to achieve a flexure-connected linkage system that guides rectilinear movement of its end-effector. The goal is a linkage design that can be reduced in size to provide a suspension for the proof masses of a MEMS gyroscope. The symmetric design of the linkage...

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...

This paper uses path synthesis techniques to design four-bar linkage modules to constrain the movement of a 3R chain. The result is a 10-bar linkage. The goal is to develop a design procedure for a robotic system that guides the human leg during the walking gait cycle. A 3R chain is designed to match the dimensions of a human leg and the two four-b...

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...

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 h...

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 perform...

This paper presents a design system for planar and spherical six-bar linkages, which is integrated with a solid modeler. The user specifies a backbone 3R chain in five task configurations in the sketch mode of the solid modeler and executes the design system. Two RR constraints are computed, which constrain the 3R chain to a single degree-of-freedo...

A cycle basis in an undirected graph is a minimal set of simple cycles whose symmetric differences include all Eulerian subgraphs of the given graph. We define a rooted cycle basis to be a cycle basis in which all cycles contain a specified root edge, and we investigate the algorithmic problem of constructing rooted cycle bases. We show that a give...

A cycle basis in an undirected graph is a minimal set of simple cycles whose symmetric differences include all Eulerian subgraphs of the given graph. We define a rooted cycle basis to be a cycle basis in which all cycles contain a specified root edge, and we investigate the algorithmic problem of constructing rooted cycle bases. We show that a give...

In this paper, we present an algorithm that automatically creates the linkage loop equations for planar one degree of freedom, 1DOF, linkages of any topology with revolute joints, demonstrated up to 8 bar. The algorithm derives the linkage loop equations from the linkage adjacency graph by establishing a rooted cycle basis through a single common e...

A synthesis technique for designing novel vehicle suspension linkages based on the Watt I six-bar is presented. The goal is to maintain near vertical alignment of the wheels to the road during cornering. The complete suspension is analyzed as a symmetric planar 12-bar linkage with ground pivots located at the contact patches. The design procedure s...

This paper formulates a methodology for designing planar eight-bar linkages for five task positions, by adding two RR constraints to a user specified 6R loop. It is known that there are 32 ways in which these constraints can be added, to yield as many as 340 different linkages. The methodology uses a random search within the tolerance zones around...

In this paper we present an algorithm that automatically creates the linkage loop equations for planar 1-DoF linkages of any topology with rotating joints, demonstrated up to 8-bars. The algorithm derives the linkage loop equations from the linkage graph by establishing a cycle basis through a single common edge. Divergent and convergent loops are...

This paper uses coupler-path synthesis to design four-bar linkage modules that constrains the movement of links in an nR serial chain. The goal is to formulate a general procedure for path-synthesis of a robotic system using four-bar linkages. A desired end-effector trajectory is transformed into a secondary trajectory that is used for nine-point s...

This paper presents a design procedure for six-bar linkages that use eight accuracy points to approximate a specified input-output function. In the kinematic synthesis of linkages, this is known as the synthesis of a function generator to perform mechanical computation. Our formulation uses isotropic coordinates to define the loop equations of the...

This chapter formulates the synthesis equations for a Watt I six-bar linkage that moves through \(N\) specified task positions. For the maximum number of positions, \(N=8\), the resulting polynomial system consists of 28 equations in 28 unknowns, which can be separated into a nine sets of variables yielding a nine-homogeneous Bezout degree of \(3.4...

This paper presents a synthesis methodology for a Stephenson II six-bar function generator that provides eight accuracy points, that is it ensures the input and output angles of the linkage match at eight pairs of specified values. A complex number formulation of the two loop equations of the linkage and a normalization condition are used to form t...

In this paper we present an algorithm applicable to the Watt I and Stephenson I six-bar linkage designs which determines if a candidate linkage moves smoothly through a desired range of input angles. Intended for use with a synthesis routine our algorithm uses the Jacobian of the linkage to determine if a linkage moves smoothly by identifying the c...

This paper presents a software system for the kinematic synthesis of useful spherical Watt I six-bar linkages that can guide a body through five task positions. The design procedure begins with the specification of a spherical 3R open chain that reaches five specified task positions. The six-bar linkage is designed by constraining the 3R spherical...

This is a presentation of kinematic fundamentals that rely on the theory of polynomials. The goal is to lay a foundation for modern computational methods that are finding success solving increasingly challenging problems in kinematic analysis and synthesis of machines, mechanisms and robots. Available at http://mechanicaldesign101.com

In this paper, five positions of a planar RPR serial chain are specified and the synthesis equations for two RR constraints are solved to obtain a six-bar linkage. Analysis of the resulting linkage determines if it moves the end-effector smoothly through the five task positions without a branch defect. The design procedure presented randomly select...

In this paper we present an algorithm to determine if a six-bar linkage that has been designed as a constrained 3R chain using Burmester Theory is usable. A usable six-bar linkage is one that moves a workpiece smoothly through a given set of task positions with actuation by one joint parameter. Our algorithm is a two-step process. First the linkage...

A review of the history of kinematics and machine theory shows a direct connection between the ability to solve polynomial systems using algebraic and numerical techniques and the advancement of the analysis and synthesis of machine systems including robots. Research challenges in kinematic synthesis, compliant mechanisms and cable and tensegrity s...

This paper presents the kinematic synthesis of a steering linkage that changes track, wheelbase, camber, and wheel height in a turn, while maintaining Ackermann geometry. Each wheel is controlled by a 5-SS platform linkage, which consists of a moving platform connected by five SS chains to the vehicle chassis. Ackermann steering geometry ensures al...

In this paper, we consider the problem of designing planar six-bar linkages which can be driven by prismatic joints at its base. We explore various ways on how two RR chains can be used to constraint a PRR planar serial chain such that the system yields one-degree of freedom yet passes through a set of five specified task positions. We formulate an...

In this paper, we consider the problem of designing mechanical constraints for a planar serial chain formed with three revolute joints, denoted as the 3R chain. Our focus is on the various ways that two RR chains can be used to constrain the links of the 3R chain such that the system has one degree-of-freedom, yet passes through a set of five speci...

In this chapter we consider spatial displacements that are pure rotations in threedimensional space. These are transformations that have the property that one point of the moving body M has the same coordinates in F before and after the displacement. Because the distance between this fixed point and points in M are constant, each point in the movin...

In this chapter we develop the geometry of spatial displacements defined by coordinate transformations consisting of spatial rotations and translations. We consider the invariants of these transformations and find that there are no invariant points. Instead there is an invariant line, called the screw axis. Thus, the geometry of lines becomes impor...

In this chapter we formulate the design theory for spherical RR chains. The axes of the two revolute joints must lie in the same plane, and therefore intersect in a point. The floating link of this system moves in pure rotation about this point.

In this chapter we formulate design equations for a spatial serial chain using the matrix exponential form of its kinematics equations. These equations define the position and orientation of the end effector in terms of rotations about the joint axes of the chain. Because the coordinates of these axes appear explicitly, we can specify a set of task...

In this chapter we examine the design of RR, PR and RP planar open chains that reach a specified set of task positions. A constraint equation is defined for each chain that characterizes the set of positions that it can reach. This relationship is inverted by considering the positions as known and the fixed and moving pivots of the chain as unknown...

In this chapter, we consider the design of spatial serial chains that guide a body such that a point in the body moves on a specific algebraic surface. The problem originates with Schoenflies [113], who sought points that remained in a given configuration for a given set of spatial displacements. Burmester [7] applied this idea to planar mechanism...

In this chapter we study spatial linkages. These systems have at least one link that moves through a general spatial displacement. We examine the TS and CC chains that are important to our design theory, as well as the TPS and TRS chains that appear in robotics. In addition, we study the 3R wrist which is actually a spherical linkage, however, it p...

In this chapter we examine spherical linkages. These linkages have the property that every link in the system rotates about the same fixed point. Thus, trajectories of points in each link lie on concentric spheres with this point as the center. Only the revolute joint is compatible with this rotational movement and its axis must pass through the fi...

JMR Editorial – May 2011 As we move into the second decade of the 21st century, we can identify three research trends that we can expect to persist into the future. They are the analysis and synthesis of (i) spatial mechanisms and robotic systems, (ii) compliant linkage systems, and (iii) tensegrity and cable-driven systems. In each case, we find t...

A metamorphic linkage has the property that the effective number of links and joints can change during the movement of the device. This means the kinematic structural representation of a metamorphic linkage has different forms in which vertices and edges combine depending on the configuration of the device. In this paper, we use the constraint grap...

JMR Editorial – February 2011 As we move into the adolescent years of the 21st century, allow me to discuss where research in mechanisms and robotics has been as a prelude to considering where it is going. Polynomials: Mechanisms have been characterized by the curves that they trace since the time of Archimedes [1]. In the 1800's, F. Reuleaux, A. B...

In this chapter, we will formulate the systematic design of multiloop planar linkages in a way that combines with traditional robotics and four-bar linkage synthesis theory to obtain innovative articulated robotic systems. First, we will show how mechanical constraints can be introduced to a planar 3R serial chain to guide the movement of its end e...

In this chapter, the design procedure introduced for the synthesis of planar six- and eight-bar linkages is applied to the synthesis of spherical six- and eight-bar linkages. The process begins with the specification of a spherical 3R chain or a spherical 6R loop and five task orientations. The synthesis equations for RR chains are solved to constr...

In this chapter we consider assemblies of links that move in parallel planes. Any one of these planes can be used to examine the movement since the trajectories of points in any link can be projected onto this plane without changing their properties. Our focus is on linkages constructed from revolute joints with axes perpendicular to RR, PR, and RP...

The geometric principles that are fundamental to linkage design can be found in simple and efficient graphical constructions for RR and PR chains. As the floating link of one of these chains reaches various task positions, points in it define sets of corresponding points in the fixed frame. The design problem is to find a circle for the RR chain an...

In this chapter we consider six-degree-of-freedom systems consisting of a platform supported by multiple serial chains, called parallel, or platform, manipulators.Walking machines, mechanical fingers manipulating an object, and vehicle simulator platforms are all examples of platform manipulators. The Jacobian of these systems defines the contribut...

This book is an introduction to the mathematical theory of design for articulated mechanical systems known as linkages. The focus is on sizing mechanical constraints that guide the movement of a workpiece, or end effector, of the system. The function of the device is prescribed as a set of positions to be reachable by the end effector; and the mech...

In this paper, we present a synthesis procedure for the coupler link of a planar slider-crank linkage in order to coordinate input by a linear actuator with the rotation of an output crank. This problem can be formulated in a manner similar to the synthesis of a five position RR coupler link. It is well-known that the resulting equations can produc...

A mechanical system, or machine, generally consists of a power source and a mechanism for the controlled use of this power. The power may originate as the flow of water or the expansion of steam that drives a turbine and rotates an input shaft to the mechanism. It may be that instead the turbine rotates a generator and the resulting electricity is...