Curtis L. Collins

The singularity analysis of an in-parallel hand controller for force-reflected teleoperation

Force-reflected teleoperation with in-parallel devices are gaining prominence in robotics applications. Although their development has been limited primarily to Stewart-platform type devices, many other in-parallel hand controllers hold promise for force-reflected manipulation. One factor prohibiting a full exploration involves their singularity analyses-use of conventional rank determining methods are overly complicated. Singularity analysis complications arise because the Jacobian matrix has several functionally dependent variables. In this analysis, we first derive the Jacobian matrix and then show its six columns can be viewed as zero-pitch wrenches (lines) acting on the top platform. We then show how line geometry and rank determining geometric constructions can be used to obtain all configuration singularities. >

A pantograph linkage parallel platform master hand controller for force-reflection

The authors discuss the kinematics of a serial/parallel six degree-of-freedom generalized hand controller for teleoperation. A description of the device is presented with equations needed for control of a remote manipulator. The pantograph linkages extend the workspace of traditional platform designs, while the parallel structure provides force regulation at the platform that is well suited for force-feedback to a teleoperator. The generalized teleoperator controller described will be part of a larger telerobotics system comprising a radio-controlled robotic arm module with appropriate end-effectors and a general-purpose supervisory controlled system. The robotic system is planned for remote handling of toxic solid and liquid debris.<<ETX>>

The quartic singularity surfaces of planar platforms in the Clifford algebra of the projective plane

Abstract In this paper, we study the workspace and singular configurations of a planar platform supported by three linearly actuated legs, the 3-RPR parallel manipulator. The constraint equations of the platform are formulated in the Clifford algebra of the projective plane, C + (P 2 ) , which yields a manifold defining its set of reachable positions and orientations. We compute the Jacobian of these equations and derive the algebraic equation of the surface of points in C + (P 2 ) for which this Jacobian is singular, called the singularity surface of the manipulator. For the general planar platform manipulator this surface is a quartic surface with a double line. For the special case of the “proportional” planar platform, the surface factors into two planes and a circular hyperboloid. For the special case of the “in-line” planar platform, this surface reduces to a quartic ruled surface. Further special cases of this surface are examined and found to consist of pairs of hyperbolic paraboloids.

An Extensible Java Applet for Spatial Linkage Synthesis

A spatial linkage is defined by a workpiece supported by several serial chains. The task of the linkage is defined by specifying rigid positions for the workpiece that approximate a desired workspace. Spatial serial chains can be synthesized and combined to form more complicated linkages. Because there are many serial chains available for this design process, we have developed a Java-based architecture for a computer-aided-design system for spatial linkages that is organized to allow incorporation of individually defined serial chain classes prepared by users/collaborators. Using the RR and TS chains as an example, we present the general features common to dimensional synthesis methodologies, and identify the types of analysis, synthesis, and evaluation routines that are required for displaying, animating, and designing spatial linkages formed from serial chain primitives. We present the basic components of the design system as well as specifications for the serial chain analysis and synthesis classes. An example is provided to demonstrate how the system can be used to perform three position synthesis of spatial RR, TS, and RRTS linkages.

Classification of RRSS linkages

This paper classifies the movement of the RRSS spatial linkage in terms of its link dimensions. The constraint equation for this chain relates the rotation angles of the input crank and coupler around the two revolute joints. The condition for a real valued solution for the coupler angle as a function of the input angle yields a quartic polynomial. We use three polynomial discriminants obtained from this quartic to find explicit conditions for the cases available for the movement of the input crank. A similar analysis characterizes the coupler movement by determining conditions that ensure real solutions for the input angle as a function of the coupler angle. Combining the results we obtain parameters that characterize movement of the RRSS linkage. Examples for the various cases are provided.

On the duality of twist/wrench distributions in serial and parallel chain robot manipulators

Duality and reciprocity between twist and wrench systems is the essence of screw theory. The power of these concepts lies in the idea that once a result is obtained for one type of system it can immediately be applied to the dual system provided the appropriate physical interpretation is also translated. The interrelation between serial and parallel mechanisms is a consequence of this twist/wrench duality. The purpose of this investigation is to focus on some fundamental configurations of serial and parallel robot manipulators in an attempt to further elucidate the various correspondences that exist between their geometries and their kinematic equations. The focus is on zero-pitch screw systems, namely revolute joints for serial manipulators and force producing sub-chains in parallel manipulators. Solutions for twist/wrench distributions will be discussed for both proper and redundant systems.

The singularity loci of two triangular parallel manipulators

We study the Jacobian of spatial parallel manipulators that have triangular base and top platform architectures with 2-2-2 and 3-2-1 actuator configurations. The Jacobian matrix is formulated using dual quaternion coordinates. The zero locus of the determinant of the resulting Jacobian is what we refer to as the singularity loci. The result is an eighth order polynomial in the dual quaternion coordinates. The loci of singular positions for a fixed orientation for the 2-2-2 actuator arrangement is a cubic surface. The loci of singular positions for the 3-2-1 actuator arrangement is also a cubic surface, which factors into three planes.

The Structure of an Extensible Java Applet for Spatial Linkage Synthesis

This paper describes a new approach to computer-aided spatial linkage design which uses the dynamic binding feature of Java to provide a extensible software system. The spatial linkages that we focus on are constructed from one or more spatial open chains that are connected to a single workpiece. Each open chain has less than six degrees of freedom and is termed a serial chain primitive. The goal of the design system is to determine the dimensions of a set of primitives each of which has a workspace that includes the set of specified workpiece positions. These chains are then assembled together to form candidate parallel linkage designs. There are many serial chain primitives each of which has a specialized constraint solver. These primitives can be assembled into many different parallel linkages, each of which needs an analysis routine. Our approach to the challenge of generating all of these routines is to abstract the design process and structure our computer-aided linkage design system to allow integration of specialize synthesis and analysis routines developed over time by user-collaborators. @DOI: 10.1115/1.1486217#

Kinematics of Robot Fingers with Circular Rolling Contact Joints

This paper examines the kinematics of robot fingers that use RR subassemblies coupled by rolling contact to provide versatile one degree-of-freedom mechanical joints. A three degree-of-freedom robot finger constructed with these joints is a 6R planar chain with the R-joints coupled together in pairs. The focus is on coupling based on pure rolling of circular cylinders which can be realized by friction contact, gearing, or cable tendons. We derive the forward, inverse and rate kinematics for this 3(RR) open chain. We then focus on the two degree-of-freedom 2(RR) case to illustrate the geometry of the system. An example design of a robot finger that incorporates these joints in order to provide compact movement is provided.

Kinematics of a Spatial Three Degree-of-Freedom Robot With Rolling Contact Joints

A rolling contact joint is formed when two adjacent links roll without slipover each other. When the rolling profiles are circular, the joint can be physically realized by a pair of revolute joints coupled by gears or cables. In this paper, we investigate the forward, inverse, and rate kinematics of a spatial three degree-of-freedom serial chain with rolling contact joints that have equal circular profiles. We show analytically and geometrically that there are 32 inverse kinematic solutions. Singularities occur whenever the point of interest on the end effector lies on either of two planes defined by the lines of contact between the joints.© 2002 ASME