Serial and Parallel Robot Manipulators - Kinematics, Dynamics, Control and Optimization

A method for force analysis of the overconstrained lower mobility parallel mechanism

This paper introduces a class of reconfigurable parallel robots consisting of a fixed base and a moving platform connected by serial chains having RRPS (Revolute-Revolute-Prismatic-Spherical) topology. Only the prismatic joint is actuated and the first revolute joint in the chain can be locked or released online. The introduction of these lockable joints allow the prismatic actuators to maneuver to approximate 6-DoF motions for the moving platform. An algorithm for generating these maneuvers is first described. Then, a motion planner, based on the generation of a Probabilistic RoadMap (PRM) whose nodes are connected using the described maneuvers, is presented. The generated trajectories avoid singularities and possible collisions between legs. (See accompanying video)

/pdf/motion-planning-for-a-novel-reconfigurable-parallel-48zvv2mys3.pdf

Motion planning for a novel reconfigurable parallel manipulator with lockable revolute joints

In order to resolve the redundancy of a wheeled mobile redundant manipulator comprising a two-wheel-drive mobile platform and a 6-degree-of-freedom manipulator, a physical-limits-constrained (PLC) minimum velocity norm (MVN) coordinating scheme (termed as PLC-MVN-C scheme) is proposed and investigated. Such a scheme can not only coordinate the mobile platform and the manipulator to fulfill the end-effector task and to achieve the desired optimal index (i.e., minimizing the norm of the rotational velocities of the wheels and the joint velocities of the manipulator) but also consider the physical limits of the robot (i.e., the joint-angle limits and joint-velocity limits of the manipulator as well as the rotational velocity limits of the wheels). The scheme is then reformulated as a quadratic program (QP) subject to equality and bound constraints, and is solved by a discrete QP solver, i.e., a numerical algorithm based on piecewise-linear projection equations (PLPE). Simulation results substantiate the efficacy and accuracy of such a PLC-MVN-C scheme and the corresponding discrete PLPE-based QP solver.

Physical-limits-constrained minimum velocity norm coordinating scheme for wheeled mobile redundant manipulators

This paper presents a new configuration for ankle rehabilitation using a 9-DOF (degree of freedom) hybrid parallel robot. The robot contains nine linear actuators serially connecting two movable platforms and one stationary platform. The optimization is based on the singularity and dynamic analysis of the robot. The obtained data of the ankle motions from a series of experiments were applied to the model in order to investigate the motion of the end-effector and the force required for each actuator in a particular path. The end-effector tracking simulation results validated the proposed theoretical analysis of the required rehabilitation path of the foot.

https://www.cambridge.org/core/services/aop-cambridge-core/content/view/25ADB3A4F31CABB651D9155A4D9F7DB6/S0263574714001210a.pdf/div-class-title-path-planning-of-the-hybrid-parallel-robot-for-ankle-rehabilitation-div.pdf

Path planning of the hybrid parallel robot for ankle rehabilitation

Kinematics/statics of a 4-DOF over-constrained parallel manipulator with 3 legs

A novel 4-dof 2SPS+SPR parallel kinematic machine is proposed, and its kinematics, statics, and workspace are studied systematically. First, the geometric constrained equations are established, and the inverse displacement kinematics is analyzed. Second, the poses of active/constrained forces are determined, and the formulae for solving inverse/forward velocities are derived. Third, the formulae for solving inverse/forward accelerations are derived. Finally, a workspace is constructed and its active/constrained forces are solved. The analytic results are verified by its simulation mechanism to be consistent with the calculated ones.

Kinematics and statics analysis of a novel 4-dof 2sps+2spr parallel manipulator and solving its workspace

A novel analytic approach is proposed for determining the singularities of some four degree of freedom (DOF) parallel manipulators (PMs). First, the constraint and displacement of a general 4-DOF PM are analyzed. Second, a common 3 × 4 translational Jacobian matrix Jν and a common 3 × 4 rotational Jacobian matrix Jω are derived, and a 4 × 4 general Jacobian matrix J of the 4-DOF PMs is derived from Jν and Jω. Since a complicated process to determine singularities from the 4 × 6 Jacobian matrix is transformed into a simple process to determine singularity from J, the singularities of the some 4-DOF PMs with 3 translations and 1 rotation, or with 3 rotations and 1 translation, or with combined translation–rotations are analyzed and determined easily by this approach.

https://www.cambridge.org/core/services/aop-cambridge-core/content/view/S0263574709990518

Determination of singularities of some 4-dof parallel manipulators by translational/rotational jacobian matrices

This paper proposes an approach for solving the velocity and acceleration of the limited-dof (dof n P R + U P U PKM and a 2S P S + R PRR PKM are illustrated for explaining how to use this method. This approach is simple because it needs neither to eliminate 6-n rows of an n × 6 Jacobian matrix nor to determine the screw or pose of the constrained wrench.

https://www.cambridge.org/core/services/aop-cambridge-core/content/view/S0263574709005396

Kinematic analysis of limited-dof parallel manipulators based on translational/rotational jacobian and hessian matrices

This paper proposes a systematic methodology for dimension synthesis, kinematics, and statics of a novel 2SPS +SPR +SP parallel manipulator with 3DOF First, a workspace is varied and analyzed by varying the orientation of a revolute joint, and an optimum orientation of revolute joint is determined. Second, the inverse displacement is analyzed, and the formulas are derived for solving general inverse/forward velocities and accelerations. Third, the geometric constraints of constrained forces are determined and the formulas are derived for solving the active/constrained forces.

Synthesis and Analysis of Kinematics/Statics of a Novel 2SP̱S+SP̱R+SP Parallel Manipulator

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