Transactions of the Canadian Society for Mechanical Engineering

Volume 31 (2007), Issue 4

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Singularities can be elusive but geometric considerations can reveal the singularities of a redundant 4R manipulator for positioning tasks. Points on a line, called transversal, that intersects all R-joint axes, cannot move in the direction of this line. Conditions governing the existence of transversals to four lines will be discussed. A way to find transversals is developed and tested with a numerical example. A possible metric, or singularity proximity measure for this type of singularity is investigated. This metric is based on the shortest distance between a line and a quadric and various methods will be proposed to solve this geometric problem.

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In this paper, a multi-objective trajectory planning system is developed for redundant manipulators. This system involves kinematic redundancy resolution, as well as robot dynamics, including actuators model. The kinematic redundancy is taken into account through a secondary criterion of joint limits avoidance. The optimization procedure is performed subject to limitations on actuator torques and workspace, while passing through imposed poses. The Augmented Lagrangian with decoupling (ALD) technique is used to solve the resulting constrained non-convex and non-linear optimal control problem. Furthermore, the final state constraint is solved using a gradient projection. Simulations on a three degrees of freedom planar redundant serial manipulator show the effectiveness of the proposed system.

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The Lagrangian approach to the development of dynamics equations for a multi-body system, constrained or otherwise, requires solving the forward kinematics of the system at velocity level in order to derive the kinetic energy of the system. The kinetic-energy expression should then be differentiated multiple times to derive the equations of motion of the system. Among these differentiations, the partial derivative of kinetic energy with respect to the system generalized coordinates is specially cumbersome. In this paper, we will derive this partial derivative using a novel kinematic relation for the partial derivative of angular velocity with respect to the system generalized coordinates. It will be shown that, as a result of the use of this relation, the equations of motion of the system are directly derived in the form of Kane's equations.

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This paper presents a mechanical analysis of a spatial 1-DOF tensegrity mechanism created by connecting three planar tensegrity mechanisms to form a triangular prism. The subsequent investigation produced kinematic and dynamic models that allow the workspace-boundary singularities and minimum energy configuration to be determined. Singularities were found to occur when the mechanism is folded in the vertical X, Y plane or in the horizontal X, Z plane. The minimum energy configuration, formed by the angle between the horizontal plane and the actuated strut, was found to be θ = π/4. However, when the system was linearized to determine the analytic solution for the dynamics, the minimum energy configuration become θ = 1 due to the inherent error produced by the system linearization. The dynamic response of the mechanism to an initial small displacement was determined for each case of critically damped, overdamped, and underdamped systems.

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In the field of tissue engineering, mechanical cell stimulators are widely used to simulate forces in natural body environments, or to accelerate the growth of tissue. Simulation of the natural body environment, in vitro, enables researchers to understand the effect of different disturbance on cells, independently. For tissue such as the cartilage, which grows relatively slow in a mature natural body environment, a cell stimulator can be used to speed up the growth of tissue. This paper presents a novel design of planar mechanical cell stimulator which is able to provide mobility of four. The stimulator was fabricated from polymethyl-methacrylate (PMMA) thin plates using advanced micromilling material-removal process with an accuracy of ±3 μm and a surface roughness of 120 nm. The kinematic model of the stimulator is developed and corresponding performance is simulated.

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It is widely claimed that parallel robots are intrinsically more accurate than serial robots because their errors are averaged instead of added cumulatively, an assertion which has not been properly addressed in the literature. This paper addresses this void by comparing the kinematic accuracy of two pairs of serial-parallel 2-DOF planar robots. Only input errors are considered and all robots are optimized for accuracy, the only constraint being that they cover a given desired workspace. The results of this comparison seem to confirm that parallel robots are less sensitive to input errors than serial robots. However, this comparison is too limited to draw any general conclusions. Besides, it is virtually impossible to make a meaningful comparison between other pairs of serial and parallel robot. Therefore, there is no simple answer to this question of superiority.

pages 457-468
Qimi Jiang, Clement M. Gosselin
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To pursue the maximal singularity-free workspace of parallel mechanisms is a very important concern for robot designers. This paper focuses on the case of planar 3-RPR parallel mechanisms. First, a relatively simple singularity equation of any point on the platform is derived. The obtained singularity equation shows that the singularity locus of any point on the platform is a circle of the same size, as long as the base and the platform are similar triangles. Furthermore, the three centres of the workspace circles lie exactly on the singularity circle. With these useful observations, the singularity-free workspace as well as the maximal leg length ranges can be determined. For a base of unit area, it is found that robots with equilateral triangle base and platform can obtain the maximal singularity-free workspace. Three case studies demonstrate this observation. Finally, a procedure for this kind of robot geometric design is provided.

pages 469-480
Flavio Firmani, Alp Zibil, Scott B. Nokleby, Ron P. Podhorodeski
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The force-moment capabilities of revolute-jointed planar parallel manipulators (PPMs) are presented. A previously developed analysis that determines explicitly the force-moment capabilities of parallel manipulators is considered and the formulation is improved. This analysis is based upon properly adjusting the actuator outputs to their maximum capabilities. The force-moment capabilities of two actuation layouts are investigated: the non-redundant 3-RRR PPM and the redundantly actuated 4-RRR PPM, where the underline indicates the actuated joint. Four studies of force-moment capabilities are presented: maximum force with a prescribed moment, maximum applicable force, maximum moment with a prescribed force, and maximum applicable moment. These studies are performed for constant payload orientation of the mobile platform throughout the manipulator's workspace. It is concluded that the manipulator with the additional actuated branch shows an improvement of the force-moment capabilities at the expense of reducing its workspace.

pages 483-494
S.M. O'Brien, J.A. Carretero, P. Last
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In this paper a new calibration strategy that does not require any sensors beyond those used to control actuators is applied to the 3-PRS parallel manipulator. Parallel manipulators have several advantages over their serial counterparts, but have seen limited use because of low accuracy, among other reasons. Calibration allows the kinematic model that is used to control the manipulator to be adjusted to more closely replicate the physical manipulator. The architecture and kinematics of the 3-PRS are presented, as well an explanation of this new calibration strategy. The strategy makes use of direct kinematic singularities to obtain the redundant information required for calibration Implementation of the algorithms accomplished via a nested series of optimization problems, each one accomplishing a simpler stage of the overall procedure. A simulated calibration is performed, and the algorithm successfully returns the exact values used to generate the test data. Parallel manipulator, calibration, singularity-based calibration.

pages 495-507
Sureyya Sabin, Leila Notash
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The kinematic modelling and analysis of a 4 degrees of freedom wire-actuated parallel manipulator with redundant actuation is investigated. The manipulator employs combinations of rigid links, joints and wires. Hybrid actuation of joints and wires, two actuated joints and three actuated wires, is used. Position and first and second order kinematics of the closed-loop manipulator are formulated based on matrix exponentials. The transfer of first and second order kinematic variables, i.e., wire/joint velocities and accelerations, among the manipulator task space coordinates, active and passive joint coordinates and wire lengths are provided.

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In this article, an experimental calibration of the constraining linkage of a wire-actuated parallel robot is discussed. The experimental test bed includes a prototyped 4 degrees of freedom wire-actuated parallel manipulator and an optical tracking system. The parallel manipulator employs hybrid actuation of joints and wires and includes a rigid branch to constrain the motion of its mobile platform in roll and yaw rotations. The kinematic calibration of the rigid branch is performed. A point-to-point path is designed for the manipulator and an optical tracking system is used as an external measuring device to track a tool attached to the mobile platform and to register the manipulator poses. The deviation between the actual (measured) pose of the mobile platform and the calculated pose (via direct kinematics using the joint encoders), which could be due to errors in the kinematic parameters, actuators and sensors, is used as the error function.

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The problem of redundancy resolution for underwater remote vehicle-manipulator systems (URVM) is addressed in the current work. In URVM applications, it is beneficial to have the underwater remote vehicle (URV) hold station using its thrusters while a human pilot operates the serial manipulator. This provides a stable platform for the manipulator and eases the pilot's job drastically when current and/or tether disturbances are present. However, when following this objective, the redundancy of the URVM as a whole is wasted; the four actively controlled motions of the URV are not used to improve the efficacy of the manipulator task, In fact, this standard operating procedure frequently puts the manipulator into near singular configurations. This is not desirable from the manipulator controller standpoint since near singular configurations result in undesirably high joint velocities and oscillations. In this work, a new heuristic approach based on the task-priority redundancy resolution scheme is applied to the URVM. The proposed approach provides a means to avoid singular configurations of the manipulator, and provides dexterous manipulation by using the URV's mobility in an optimal, coordinated manner. This scheme is particularly useful for remote systems where an a priori trajectory generator is not applicable. Numerical case studies are developed to demonstrate the effectiveness of the technique.

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This work presents the analysis, simulation, design, and assembly of a three-degree-of-freedom reconfigurable robotic arm. Unlike conventional reconfigurable robots, the final design illustrated in this paper does not achieve re-configurability through modular joints; instead, it is equipped with passive telescopic joints. These passive joints allow the robotic arm to change its Denavit-Hartenberg parameters via an innovative braking system. The robotic arm itself presents many advantages; not only is it versatile to perform various tasks, but it can be packed into a small volume, as usually required for launch in space applications.

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Conventional Mars rover designs incorporate complicated drive systems. In order to reduce weight, complexity and power consumption, it may be beneficial to consolidate the orthogonal functions of wheel-walking and steering into a single drive. The simultaneous operation of both steering and wheel-walking is not required. This paper demonstrates the concept of a dual-axis drive through the design and construction of a scaled prototype. The final design is novel in employing a linear actuator which is eccentric to both axes of motion. A switching and locking mechanism provides transfer between the two different functions at multiple angular positions.

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There has been considerable interest in the unmanned exploration of Mars for quite some time [4][7][8] but the current generation of rovers can explore only a small portion of the total planetary surface. One approach to addressing this deficiency is to consider a rover that has greater range and that is cheaper so that it can be deployed in greater numbers. The option explored in this paper uses the wind to propel a rover platform, trading off precise navigation for greater range. The capabilities of such a rover lie between the global perspective of orbiting satellites and the detailed local analysis of current-generation rovers. The design of the Wind-Powered Mars Rover is discussed, and the prototype built at McGill University as part of a student design course is described.