A local definition of fault tolerance, based on properties of the manipulator Jacobian, is used to generate the kinematics of seven degree-of-freedom (DOF) revolute joint manipulators. The measure of fault tolerance used is the smallest singular value over all possible Jacobians resulting from single locked joint failures. The canonical form for an optimal fault-tolerant Jacobian that maximizes this measure has been previously identified. It has also been known that it is not possible to generate a seven DOF revolute manipulator that corresponds to this theoretically optimal Jacobian. However, in this paper, it is shown how to generate physically realizable Jacobians that are very close to being optimal. It is further shown that there exist 7! different manipulators, from a single Jacobian, that have the same local fault tolerance properties. To evaluate the global properties of these different manipulators, a technique for computing six-dimensional fault-tolerant workspaces is presented. The size of these workspaces vary significantly among these 7! manipulators.

It is well known that anthropomorphic manipulators, such as the PA-10, are intolerant to a single locked joint failure of the elbow. This is because the elbow is the only joint that can change the distance between the spherical shoulder joint and the spherical wrist. In this work, it is shown how such arms can be made significantly more fault tolerant by a minor modification to the kinematic structure of the arm. We quantify the degree of fault tolerance to locked joint failures as the minimum of the smallest singular value of the resulting seven Jacobians over all possible single failures. The DH parameters for the modified arm are designed so that the corresponding fault tolerant properties are close to those of a robot with an optimally failure tolerant Jacobian. The fault tolerance of the designed robot is evaluated for two different classes of applications, i.e., point-to-point motions and specified end-effector trajectories.

Kinematically redundant manipulators are inherently more robust to locked joint failures than non-redundant manipulators. However, if poorly designed, performance degradation may still occur in the presence of a single locked joint. This paper presents a technique for designing a desired operating workspace for a kinematically redundant manipulator that can be guaranteed after the occurrence of an arbitrary single locked joint failure. The existence of such a workspace, called a failure-tolerant workspace, will be guaranteed by imposing a suitable set of artificial joint limits prior to a failure. Conditions are presented that characterize end-effector locations within the failure-tolerant region. Based on these conditions, an algorithm for computing the failure-tolerant workspace is presented. The algorithm is based upon identifying the boundaries of the failure-tolerant workspace. Examples are presented to illustrate the application of the proposed algorithm to various manipulator design problems.

It is common practice to design a robot's kinematics from the desired properties that are locally specified by a manipulator Jacobian. For the case of local optimality with respect to fault tolerance, one common definition is that the post-failure Jacobian possesses the largest possible minimum singular value over all possible locked-joint failures. This work considers the global analysis of seven-joint manipulators that have been designed to be locally optimal in terms of fault tolerance when used for six-dimensional tasks. An algorithm for calculating a six-dimensional volume that is composed of a three-dimensional positioning component and a three-dimensional orientation component is presented. Two example manipulators are then analyzed and compared, illustrating a wide degree of variability between their global fault tolerant properties. It is further shown that there are 7! = 5040 different such manipulator designs due to the number of permutations of the Jacobian matrix.

It is common practice to design a robot's kinematics from the desired properties that are locally specified by a manipulator Jacobian. In this work, the desired property is fault tolerance, defined as the post-failure Jacobian possessing the largest possible minimum singular value over all possible locked-joint failures. A mathematical analysis based on the Gram matrix that describes the number of possible planar robot designs for optimally fault-tolerant Jacobians is presented. It is shown that rearranging the columns of the Jacobian or multiplying one or more of the columns of the Jacobian by ±1 will not affect local fault tolerance; however, this will typically result in a very different manipulator. Two examples, one that is optimal to a single joint failure and the second that is optimal to two joint failures, are analyzed. This analysis shows that there is a large variability in the global kinematic properties of these designs, despite being generated from the same Jacobian. It is especially surprising that major differences in global behavior occurs for manipulators that are identical in the working area.

This work presents a method for identifying all the kinematic designs of spatial positioning manipulators that are optimally fault tolerant in a local sense. We use a common definition of fault tolerance, i.e., the post-failure Jacobian possesses the largest possible minimum singular value over all possible single locked-joint failures. The large family of physical manipulators that can achieve this optimally failure tolerant configuration is then parameterized and categorized. We develop a general computational technique to evaluate the resulting manipulators in terms of their global kinematic properties, with an emphasis on failure tolerance. Several manipulators with a range of desirable kinematic properties are presented and analyzed, with a specific example of optimizing over a given class of manipulators that possess a specified kinematic constraint.

It is common practice to design a robot's kinematics from the desired properties that are locally specified by a manipulator Jacobian. It has been recently shown that multiple different physical robot kinematic designs can be obtained from (essentially) a single Jacobian that has desirable fault tolerant properties. Fault tolerance in this case is defined as the post-failure Jacobian possessing the largest possible minimum singular value over all possible locked-joint failures. In this work, a mathematical analysis that describes the number of possible planar robot designs for optimally fault-tolerant Jacobians is presented. Two examples, one that is optimal to a single joint failure and the second that is optimal to two joint failures, are discussed. The paper concludes by illustrating some of the large variability in the global kinematic properties of these designs, despite being generated from the same Jacobian.

It is common practice to design a robot's kinematics from the desired properties that are locally specified by a manipulator Jacobian. For the case of optimality with respect to fault tolerance, one common definition is that the post-failure Jacobian possesses the largest possible minimum singular value over all possible locked-joint failures. This work considers a Jacobian that has been designed to be optimally fault tolerant for a simple spatial positioning manipulator. It is shown that despite the fact that the Jacobian is “unique”, up to column permutations and multiplications by ±1, there are a large family of physical manipulators that correspond to the optimal Jacobian. Two example manipulators are presented and analyzed. It is shown that there is a large degree of variability in the global kinematic properties of these designs, despite being generated from the same Jacobian.