A Novel Three-loop Parallel Robot with Full Mobility: Kinematics and Singularity Analysis

[+] Author and Article Information
Wei Li

PhD candidate, Department of Mechanical Engineering and Centre for Intelligent Machines, McGill University, Montreal, QC, H3A 0C3 Canada

Jorge Angeles

Professor, Fellow of ASME, Department of Mechanical Engineering and Centre for Intelligent Machines, McGill University, Montreal, QC, H3A 0C3 Canada

1Corresponding author.

ASME doi:10.1115/1.4037112 History: Received October 03, 2016; Revised June 10, 2017


A novel parallel robot, dubbed the SDelta, is the subject of this paper. The robot is a simpler alternative to both the well-known Stewart-Gough platform (SGP) and current three-limb, full-mobility parallel robots, as it contains fewer components and all its motors are located on the base, which greatly reduces the inertial load on the system, making it a good candidate for high-speed operations. SDelta features a symmetric structure; its forward-displacement analysis leads to a system of three quadratic equations in three unknowns, the robot direct-kinematics thus admitting up to eight solutions, or half the number of those admitted by the SGP. The kinematic analysis, undertaken with a geometrical method based on screw theory, leads to two Jacobian matrices, whose singularity conditions are investigated. Instead of using the determinant of a 6×6 matrix, we derive one simple expression that characterizes the singularity condition. This approach is also applicable to a large number of parallel robots whose six actuation wrench axes intersect pairwise, such as the SGP and three-limb parallel robots whose limbs include, each, a passive spherical joint. The workspace is analyzed via a geometric method, while the dexterity analysis is conducted via a discretization method. Both show that the given robot has the potential to offer both large workspace and good dexterity with a proper choice of design variables.

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