American Society of Mechanical Engineers eBooks, 1994
One of three volumes resulting from the 23rd Biennial ASME Mechanisms Conference, this volume con... more One of three volumes resulting from the 23rd Biennial ASME Mechanisms Conference, this volume contains papers on topics in computational kinematics of spatial mechanisms, type synthesis of mechanisms, planar mechanism analysis, computational kinematic synthesis of spatial mechanisms, synthesis of sp
American Society of Mechanical Engineers eBooks, 1994
The September 1994 conference was organized by the Mechanisms Committee of the Design Engineering... more The September 1994 conference was organized by the Mechanisms Committee of the Design Engineering Division, ASME, under the auspices of the Design Technology Conference. The papers in this volume address topics in vibrational robotic systems, elasto-dynamics of mechanisms, design of machine elements
ABSTRACT Screw theory is applied to the inverse static force problem of a general geometry, six-d... more ABSTRACT Screw theory is applied to the inverse static force problem of a general geometry, six-degree-of-freedom, three-cylindric robot. The paper shows that the transpose of the (3 × 3) dual-Jacobian matrix plays the same role in the inverse static force problem as the inverse of the matrix plays in the inverse velocity problem. The symmetry between the two solutions is discussed and shown to be a direct result of the theorem of reciprocity between the velocity screw of the end-effector and the external wrench acting on the end-effector. The paper then presents the dual actuator force applied at each of the three cylindric joints and the power required by each rotary-linear actuator to support a specified external wrench acting on the end-effector. Finally, the results are applied to a kinematically simple three-cylindric robot and a numerical example is included for illustrative purposes.
<jats:title>Abstract</jats:title> <jats:p>This paper establishes a systematic p... more <jats:title>Abstract</jats:title> <jats:p>This paper establishes a systematic procedure to determine the instantaneous invariants for a member in a planar mechanism and the curvature ratios of the path of a point fixed in the member. Closed-form expressions are derived for the instantaneous invariants and the curvature ratios as continuous functions of the input variable of the mechanism. The methods that are proposed in this paper can be applied to the design of planar mechanisms in general. For a given mechanism, the configuration defined by the input variable at which the member achieves the optimal approximation of a prescribed rigid motion can be determined. Alternatively, a point fixed in a member can be selected such that it will generate a trajectory matching a given curve with high precision. For purposes of illustration, the paper details the analytical procedure for a simple epicyclic gear train and a four-bar mechanism. The instantaneous invariants and the curvature ratios are generated for the complete operating cycle of each mechanism.</jats:p>
The secondary instantaneous centers of velocity for two-degree-of-freedom planar linkages must li... more The secondary instantaneous centers of velocity for two-degree-of-freedom planar linkages must lie on straight lines. For many of these linkages, however, some of these lines cannot be obtained by a direct application of the Aronhold-Kennedy theorem. This paper, therefore, will present both graphical and analytical techniques to locate these unknown lines of centers for certain types of two-degree-of-freedom linkages. First the techniques are applied to the three topologies of the seven-bar linkage, two of which contain a four-bar chain, and the unknown lines of centers are obtained for each topology. Then the techniques are applied to the 35 topologies of the nine-bar linkage. The paper includes a discussion of these topologies and presents three examples for illustrative purposes. The techniques can locate the unknown lines of centers for all, but one, of the 35 topologies. The techniques presented in this paper provide geometric insight into the first-order instantaneous kinematics of two-degree-of-freedom planar linkages.
The paper begins with a graphical technique to locate the pole; i.e., the point in the plane of m... more The paper begins with a graphical technique to locate the pole; i.e., the point in the plane of motion which is coincident with the instantaneous center of zero velocity of the coupler link. Since the single flier linkage is indeterminate, the Aronhold-Kennedy theorem cannot locate this instantaneous center of zero velocity. The technique that is presented here is believed to be an original contribution to the kinematics literature and will provide geometric insight into the velocity analysis of an indeterminate linkage. The paper then presents an analytical method, referred to as the method of kinematic coefficients, to determine the radius of curvature and the center of curvature of the path traced by an arbitrary coupler point of the single flier eight-bar linkage. This method has proved useful in curvature theory since it separates the geometric effects of the linkage from the operating speed of the linkage.
This paper presents the forward position analysis of two planar three degree-of-freedom robots, w... more This paper presents the forward position analysis of two planar three degree-of-freedom robots, with all revolute joints, manipulating a single degree-of-freedom closed-loop linkage payload. Kinematic constraint relations are developed which provide geometric insight into the cooperating robot-payload system and are important in the control of the two robots. For illustrative purposes, the payload that is considered here is a planar four-bar linkage. The paper shows that the orientation of a specified link in the payload can be described by a sixth-order polynomial. This polynomial is an important contribution, not only to the kinematics of the cooperating robots, but to the multiple-input closed-loop nine-bar linkage formed by the two robots and the payload. The polynomial contains important information regarding the assembly configurations and the stationary configurations of the system. The paper shows that zero, two, four, or six assembly configurations are possible and that each configuration corresponds to a different circuit of the system. Graphical methods are utilized to provide geometric insight into the assembly and stationary configurations and to check the results obtained from the sixth-order polynomial. A numerical example is included which demonstrates the importance of the polynomial in solving the forward position problem, and in determining the number of assembly configurations.
Geometric relationships between the velocity screw and momentum screw are presented, and the dual... more Geometric relationships between the velocity screw and momentum screw are presented, and the dual angle between these two screws is shown to provide important insight into the kinetics of a rigid body. Then the centripetal screw is defined, and the significance of this screw in a study of the dynamics of a rigid body is explained. The dual-Euler equation, which is the dual form of the Newton-Euler equations of motion, is shown to be a spatial triangle. The vertices of the triangle are the centripetal screw, the time rate of change of momentum screw, and the force screw. The sides of the triangles are three dual angles between the three vertices. The spatial triangle provides valuable geometrical insight into the dynamics of a rigid body and is believed to be a meaningful alternative to existing analytical techniques. The authors believe that the work presented in this paper will prove useful in a dynamic analysis of closed-loop spatial mechanisms and multi-rigid body open-chain systems.
Abstract This paper presents solutions to the forward and inverse velocity problems of two planar... more Abstract This paper presents solutions to the forward and inverse velocity problems of two planar 3-R robots manipulating a single rigid payload. The payload, referred to a disk, is contrained to roll between the terminal link of each robot forming a closed-loop system with a mobility of five. The forward velocity problem is solved by using the method of kinematic coefficients and the principle of superposition which models the system as five instantaneous four-bar linkages. The kinematic coefficients, which are a function of position only, provide valuable geometric insight into the instantaneous configurations of the system. A graphical method, which utilizes the instantaneous centers of zero velocity, is presented as a check of the analytical solution. Then the inverse velocity problem is formulated in terms of a Jacobian matrix whose elements are the kinematic coefficients. In addition to the solutions for the general system of mobility five, solutions are also presented for two special systems of mobility four and three. The methods presented in this paper provide insight into the analysis and the design of multiple-degree-of-freedom planar mechanisms, such as robotic fingers, which utilize the rolling contact constraint. The results are believed to be important in the trajectory planning of two robots which are cooperating with a payload that is constrained by rolling contact. For purpose of illustration, a numerical example of the general system and the two special systems is included in the paper.
This paper uses an analytical approach, based on (3×3) orthogonal transformation matrices with du... more This paper uses an analytical approach, based on (3×3) orthogonal transformation matrices with dual number elements and the principle of transference, to obtain three parametric equations for the coupler curves of the RCCC four-bar mechanism. The equations express the Cartesian coordinates of an arbitrary point fixed in the coupler link as a function of a single variable; namely, the input angle. From this systematic approach, the curve describing the path of the coupler point is shown to be 16th-order. The coupler curve equations for the spherical four-bar and the Bennett linkage are deduced as special cases. The paper then presents plots of coupler curves of a general geometry and a special geometry RCCC mechanism. The latter example has a branch extending to infinity which is directly related to the limiting positions of the mechanism. Finally, the paper includes plots of typical coupler curves of the spherical four-bar and the Bennett linkage.
ASME 1994 Design Technical Conferences collocated with the ASME 1994 International Computers in Engineering Conference and Exhibition and the ASME 1994 8th Annual Database Symposium, Mar 12, 2021
This paper presents a robotic die polishing station controlled by a PC and a robot controller. Th... more This paper presents a robotic die polishing station controlled by a PC and a robot controller. The station consists of a six-degree-of-freedom industrial robot manipulator, a pneumatic grinding tool, and grinding abrasives. The station also includes an automatic tool changer which is specifically designed to exchange the grinding tool such that the operation is completely unmanned. Since die and mold manufacturing is typically low volume production, it is not practical to use a robotic automation system and manually program the serial robot with a teach pendant. Therefore, this paper proposes a procedure where the path data for the robot end-effector is generated automatically from the NC data of a previous die or mold machining process. A PC automatically generates a program for the die or mold polishing process and this program is uploaded to the robot controller. The program not only includes the path data, but can generate several polishing patterns and will control the automatic tool changer. To improve the quality of the finish, the posture angle between the grinding tool and the surface of the part is computer-controlled. Also, to further enhance the performance of the system; i.e., to improve the grinding contact, an elastic material is inserted between the polishing pad and the holder.
The use of a computer-controlled multirobot system with sensors in batch manufacturing and assemb... more The use of a computer-controlled multirobot system with sensors in batch manufacturing and assembly tasks offers a number of significant advantages. These include cost savings, reliability, tolerance of working environments unacceptable to humans, and an adaptability to both structured and unstructured environments through simple reprogramming. The end results are improved productivity, efficiency, and flexibility in manufacturing and automation. However, the use of two or more cooperating robots has not been fully exploited to date. Current industrial practice employs simple time-space coordination which does not allow more than one robot working in a common workspace, such coordination and control results in under-utilization of robots. With the increasing demand for high performance manipulators and efficient multirobot manufacturing cells, there is a vital need to develop theoretical and design methodologies that will solve the generic problems faced by industrial robots working cooperatively. If multirobot systems are to be used in manufacturing and assembly tasks, a thorough knowledge of the dynamics of such systems is essential. This paper formulates the dynamics of two robots cooperating to move a rigid body object. The analysis is based on Newtonian mechanics with screw calculus and dual transformation matrices.
The trajectory of a robot end-effector is completely described by a ruled surface and a spin angl... more The trajectory of a robot end-effector is completely described by a ruled surface and a spin angle about the ruling of the ruled surface. In this way the differential properties of motion of the end-effector are obtained from the well-known curvature theory of a ruled surface. The robot can then be programmed so that the end-effector will follow the prescribed trajectory with high accuracy. In the case where the ruled surface can not be described by an explicit analytic function, the ruled surface may be represented by a geometric modeling technique. Since a ruled surface can be expressed in terms of a single parameter, a curve generating technique is used to represent the ruled surface. The technique presented in this paper is the Ferguson curve model which guarantees that the trajectory will pass through all of the set points and will have curvature continuity at each set point. To illustrate the proposed method of robot trajectory planning, a practical example is included in the paper.
American Society of Mechanical Engineers eBooks, 1994
One of three volumes resulting from the 23rd Biennial ASME Mechanisms Conference, this volume con... more One of three volumes resulting from the 23rd Biennial ASME Mechanisms Conference, this volume contains papers on topics in computational kinematics of spatial mechanisms, type synthesis of mechanisms, planar mechanism analysis, computational kinematic synthesis of spatial mechanisms, synthesis of sp
American Society of Mechanical Engineers eBooks, 1994
The September 1994 conference was organized by the Mechanisms Committee of the Design Engineering... more The September 1994 conference was organized by the Mechanisms Committee of the Design Engineering Division, ASME, under the auspices of the Design Technology Conference. The papers in this volume address topics in vibrational robotic systems, elasto-dynamics of mechanisms, design of machine elements
ABSTRACT Screw theory is applied to the inverse static force problem of a general geometry, six-d... more ABSTRACT Screw theory is applied to the inverse static force problem of a general geometry, six-degree-of-freedom, three-cylindric robot. The paper shows that the transpose of the (3 × 3) dual-Jacobian matrix plays the same role in the inverse static force problem as the inverse of the matrix plays in the inverse velocity problem. The symmetry between the two solutions is discussed and shown to be a direct result of the theorem of reciprocity between the velocity screw of the end-effector and the external wrench acting on the end-effector. The paper then presents the dual actuator force applied at each of the three cylindric joints and the power required by each rotary-linear actuator to support a specified external wrench acting on the end-effector. Finally, the results are applied to a kinematically simple three-cylindric robot and a numerical example is included for illustrative purposes.
<jats:title>Abstract</jats:title> <jats:p>This paper establishes a systematic p... more <jats:title>Abstract</jats:title> <jats:p>This paper establishes a systematic procedure to determine the instantaneous invariants for a member in a planar mechanism and the curvature ratios of the path of a point fixed in the member. Closed-form expressions are derived for the instantaneous invariants and the curvature ratios as continuous functions of the input variable of the mechanism. The methods that are proposed in this paper can be applied to the design of planar mechanisms in general. For a given mechanism, the configuration defined by the input variable at which the member achieves the optimal approximation of a prescribed rigid motion can be determined. Alternatively, a point fixed in a member can be selected such that it will generate a trajectory matching a given curve with high precision. For purposes of illustration, the paper details the analytical procedure for a simple epicyclic gear train and a four-bar mechanism. The instantaneous invariants and the curvature ratios are generated for the complete operating cycle of each mechanism.</jats:p>
The secondary instantaneous centers of velocity for two-degree-of-freedom planar linkages must li... more The secondary instantaneous centers of velocity for two-degree-of-freedom planar linkages must lie on straight lines. For many of these linkages, however, some of these lines cannot be obtained by a direct application of the Aronhold-Kennedy theorem. This paper, therefore, will present both graphical and analytical techniques to locate these unknown lines of centers for certain types of two-degree-of-freedom linkages. First the techniques are applied to the three topologies of the seven-bar linkage, two of which contain a four-bar chain, and the unknown lines of centers are obtained for each topology. Then the techniques are applied to the 35 topologies of the nine-bar linkage. The paper includes a discussion of these topologies and presents three examples for illustrative purposes. The techniques can locate the unknown lines of centers for all, but one, of the 35 topologies. The techniques presented in this paper provide geometric insight into the first-order instantaneous kinematics of two-degree-of-freedom planar linkages.
The paper begins with a graphical technique to locate the pole; i.e., the point in the plane of m... more The paper begins with a graphical technique to locate the pole; i.e., the point in the plane of motion which is coincident with the instantaneous center of zero velocity of the coupler link. Since the single flier linkage is indeterminate, the Aronhold-Kennedy theorem cannot locate this instantaneous center of zero velocity. The technique that is presented here is believed to be an original contribution to the kinematics literature and will provide geometric insight into the velocity analysis of an indeterminate linkage. The paper then presents an analytical method, referred to as the method of kinematic coefficients, to determine the radius of curvature and the center of curvature of the path traced by an arbitrary coupler point of the single flier eight-bar linkage. This method has proved useful in curvature theory since it separates the geometric effects of the linkage from the operating speed of the linkage.
This paper presents the forward position analysis of two planar three degree-of-freedom robots, w... more This paper presents the forward position analysis of two planar three degree-of-freedom robots, with all revolute joints, manipulating a single degree-of-freedom closed-loop linkage payload. Kinematic constraint relations are developed which provide geometric insight into the cooperating robot-payload system and are important in the control of the two robots. For illustrative purposes, the payload that is considered here is a planar four-bar linkage. The paper shows that the orientation of a specified link in the payload can be described by a sixth-order polynomial. This polynomial is an important contribution, not only to the kinematics of the cooperating robots, but to the multiple-input closed-loop nine-bar linkage formed by the two robots and the payload. The polynomial contains important information regarding the assembly configurations and the stationary configurations of the system. The paper shows that zero, two, four, or six assembly configurations are possible and that each configuration corresponds to a different circuit of the system. Graphical methods are utilized to provide geometric insight into the assembly and stationary configurations and to check the results obtained from the sixth-order polynomial. A numerical example is included which demonstrates the importance of the polynomial in solving the forward position problem, and in determining the number of assembly configurations.
Geometric relationships between the velocity screw and momentum screw are presented, and the dual... more Geometric relationships between the velocity screw and momentum screw are presented, and the dual angle between these two screws is shown to provide important insight into the kinetics of a rigid body. Then the centripetal screw is defined, and the significance of this screw in a study of the dynamics of a rigid body is explained. The dual-Euler equation, which is the dual form of the Newton-Euler equations of motion, is shown to be a spatial triangle. The vertices of the triangle are the centripetal screw, the time rate of change of momentum screw, and the force screw. The sides of the triangles are three dual angles between the three vertices. The spatial triangle provides valuable geometrical insight into the dynamics of a rigid body and is believed to be a meaningful alternative to existing analytical techniques. The authors believe that the work presented in this paper will prove useful in a dynamic analysis of closed-loop spatial mechanisms and multi-rigid body open-chain systems.
Abstract This paper presents solutions to the forward and inverse velocity problems of two planar... more Abstract This paper presents solutions to the forward and inverse velocity problems of two planar 3-R robots manipulating a single rigid payload. The payload, referred to a disk, is contrained to roll between the terminal link of each robot forming a closed-loop system with a mobility of five. The forward velocity problem is solved by using the method of kinematic coefficients and the principle of superposition which models the system as five instantaneous four-bar linkages. The kinematic coefficients, which are a function of position only, provide valuable geometric insight into the instantaneous configurations of the system. A graphical method, which utilizes the instantaneous centers of zero velocity, is presented as a check of the analytical solution. Then the inverse velocity problem is formulated in terms of a Jacobian matrix whose elements are the kinematic coefficients. In addition to the solutions for the general system of mobility five, solutions are also presented for two special systems of mobility four and three. The methods presented in this paper provide insight into the analysis and the design of multiple-degree-of-freedom planar mechanisms, such as robotic fingers, which utilize the rolling contact constraint. The results are believed to be important in the trajectory planning of two robots which are cooperating with a payload that is constrained by rolling contact. For purpose of illustration, a numerical example of the general system and the two special systems is included in the paper.
This paper uses an analytical approach, based on (3×3) orthogonal transformation matrices with du... more This paper uses an analytical approach, based on (3×3) orthogonal transformation matrices with dual number elements and the principle of transference, to obtain three parametric equations for the coupler curves of the RCCC four-bar mechanism. The equations express the Cartesian coordinates of an arbitrary point fixed in the coupler link as a function of a single variable; namely, the input angle. From this systematic approach, the curve describing the path of the coupler point is shown to be 16th-order. The coupler curve equations for the spherical four-bar and the Bennett linkage are deduced as special cases. The paper then presents plots of coupler curves of a general geometry and a special geometry RCCC mechanism. The latter example has a branch extending to infinity which is directly related to the limiting positions of the mechanism. Finally, the paper includes plots of typical coupler curves of the spherical four-bar and the Bennett linkage.
ASME 1994 Design Technical Conferences collocated with the ASME 1994 International Computers in Engineering Conference and Exhibition and the ASME 1994 8th Annual Database Symposium, Mar 12, 2021
This paper presents a robotic die polishing station controlled by a PC and a robot controller. Th... more This paper presents a robotic die polishing station controlled by a PC and a robot controller. The station consists of a six-degree-of-freedom industrial robot manipulator, a pneumatic grinding tool, and grinding abrasives. The station also includes an automatic tool changer which is specifically designed to exchange the grinding tool such that the operation is completely unmanned. Since die and mold manufacturing is typically low volume production, it is not practical to use a robotic automation system and manually program the serial robot with a teach pendant. Therefore, this paper proposes a procedure where the path data for the robot end-effector is generated automatically from the NC data of a previous die or mold machining process. A PC automatically generates a program for the die or mold polishing process and this program is uploaded to the robot controller. The program not only includes the path data, but can generate several polishing patterns and will control the automatic tool changer. To improve the quality of the finish, the posture angle between the grinding tool and the surface of the part is computer-controlled. Also, to further enhance the performance of the system; i.e., to improve the grinding contact, an elastic material is inserted between the polishing pad and the holder.
The use of a computer-controlled multirobot system with sensors in batch manufacturing and assemb... more The use of a computer-controlled multirobot system with sensors in batch manufacturing and assembly tasks offers a number of significant advantages. These include cost savings, reliability, tolerance of working environments unacceptable to humans, and an adaptability to both structured and unstructured environments through simple reprogramming. The end results are improved productivity, efficiency, and flexibility in manufacturing and automation. However, the use of two or more cooperating robots has not been fully exploited to date. Current industrial practice employs simple time-space coordination which does not allow more than one robot working in a common workspace, such coordination and control results in under-utilization of robots. With the increasing demand for high performance manipulators and efficient multirobot manufacturing cells, there is a vital need to develop theoretical and design methodologies that will solve the generic problems faced by industrial robots working cooperatively. If multirobot systems are to be used in manufacturing and assembly tasks, a thorough knowledge of the dynamics of such systems is essential. This paper formulates the dynamics of two robots cooperating to move a rigid body object. The analysis is based on Newtonian mechanics with screw calculus and dual transformation matrices.
The trajectory of a robot end-effector is completely described by a ruled surface and a spin angl... more The trajectory of a robot end-effector is completely described by a ruled surface and a spin angle about the ruling of the ruled surface. In this way the differential properties of motion of the end-effector are obtained from the well-known curvature theory of a ruled surface. The robot can then be programmed so that the end-effector will follow the prescribed trajectory with high accuracy. In the case where the ruled surface can not be described by an explicit analytic function, the ruled surface may be represented by a geometric modeling technique. Since a ruled surface can be expressed in terms of a single parameter, a curve generating technique is used to represent the ruled surface. The technique presented in this paper is the Ferguson curve model which guarantees that the trajectory will pass through all of the set points and will have curvature continuity at each set point. To illustrate the proposed method of robot trajectory planning, a practical example is included in the paper.
Uploads
Papers by gordon pennock