Non-overconstrained Mechanisms Research Articles

Configuration Design of Single-Loop Non-overconstrained Mechanism with Inactive Joints

In order to weaken the strict geometric constraint relationship between the axes of joints so as to reduce manufacturing/assembling errors of overconstrained mechanism, a configuration design methodology for single-loop non-overconstrained mechanism with inactive joints is proposed in this paper based on the screw theory. After completing analysis of degrees of freedom, the design principle and corresponding process of single-loop non-overconstrained mechanism with inactive joints are presented. By introducing two inactive R (R: single-degree-of-freedom revolute joint) joints to an active R joint of Goldberg overconstrained mechanism, the corresponding Goldberg non-overconstrained mechanism is obtained. It is verified that the velocities of two inactive joints in the Goldberg non-overconstrained mechanism are zero via investigating motion screws of branches. By further solving input and output kinematic parameters of Goldberg non-overconstrained mechanism, it is discovered that the overconstrained mechanism and corresponding non-overconstrained mechanism have the identical input–output relationship. Above results confirm that the overconstrained mechanism and its non-overconstrained counterpart with inactive joints are completely equivalent kinematically, which thereby demonstrate fully correctness of the configuration design principle and method of single-loop non-overconstrained mechanism proposed in this paper.

A calibration method for overconstrained spatial translational parallel manipulators

Abstract A calibration method for overconstrained spatial translational parallel mechanisms is proposed. The calibration of a Tri-pyramid overconstrained parallel robot is used as a vehicle to demonstrate the methodology and verify its feasibility. The proposed methodology consists of transforming the overconstrained mechanism of the robot into a non-overconstrained mechanism by replacing its redundant constraints with generalized forces (couples). The kinematic model of the non-overconstrained mechanism is derived using vector loops while its mechanical model is established by the energy method. An integrated kinematic model of the original overconstrained parallel robot is subsequently established by expressing the actual position of the end effector as the sum of the position derived by the kinematic model of the non-overconstrained mechanism and of the force-induced deformations at the end effector derived from the mechanical model. To assess the feasibility and the attainable improvements in accuracy through calibration, the positions of the end effector of the Tri-pyramid robot were measured by a method that uses a Double Ball Bar (DBB) and a 3-axes linear stage with micrometers. Based on the integrated kinematic model of the robot and the measured data, its structural parameters were identified by the Newton–Raphson iteration and least squares methods to complete the calibration. The calibration result shows that accuracy improvements on the order of 90% are achievable.

Kinematic analysis of a single-loop reconfigurable 7R mechanism with multiple operation modes

SUMMARYThis paper presents a novel one-degree-of-freedom (1-DOF) single-loop reconfigurable 7R mechanism with multiple operation modes (SLR7RMMOM), composed of seven revolute (R) joints, via adding a revolute joint to the overconstrained Sarrus linkage. The SLR7RMMOM can switch from one operation mode to another without disconnection and reassembly, and is a non-overconstrained mechanism. The algorithm for the inverse kinematics of the serial 6R mechanism using kinematic mapping is adopted to deal with the kinematic analysis of the SLR7RMMOM. First, a numerical method is applied and an example is given to show that there are 13 sets of solutions for the SLR7RMMOM, corresponding to each input angle. Among these solutions, nine sets are real solutions, which are verified using both a computer-aided design (CAD) model and a prototype of the mechanism. Then an algebraic approach is also used to analyse the mechanism and same results are obtained as the numerical one. It is shown from both numerical and algebraic approaches that the SLR7RMMOM has three operation modes: a translational mode and two 1-DOF planar modes. The transitional configurations among the three modes are also identified.

Type synthesis of spatial mechanisms for forging manipulators

In this study, a systematic method is proposed to synthesize the parallel and hybrid serial–parallel mechanisms for the forging manipulators based on the screw theory. First, several typical configurations of five-degrees-of-freedom parallel mechanism for the forging manipulators are synthesized, and they are all non-overconstrained mechanisms. Then, two kinds of hybrid serial–parallel mechanisms for the forging manipulators with the advantages of motion decoupling are constructed, which are also not overconstrained. The configurations obtained in this study would provide more type selection for the heavy-duty forging manipulators in engineering.

Kinematic Analysis and Synthesis of a 3-URU Pure Rotational Parallel Mechanism with Respect to Singularity and Workspace

This paper concerns kinematics and dimensional synthesis of a three universal-revolute-universal (3-URU) pure rotational parallel mechanism. The mechanism is composed of a base, a platform and three symmetric limbs consisting of U-R-U joints. This mechanism is a spatial non-overconstrained mechanism with three degrees of freedom. The joints in each limb are so arranged to perform pure rotational motion of the platform around a specific point. Equations for inverse displacement analysis and singularities were derived to investigate the relationship of the kinematic constants to the solution of the inverse kinematics and singularities. Based on the results, a dimensional synthesis procedure for the 3-URU parallel mechanism considering singularities and the workspace was proposed. A numerical example was also presented to illustrate the synthesis method.