Kinematic Design of a New Four Degree-of-Freedom Parallel Robot for Knee Rehabilitation

Abstract

Rehabilitation robots are increasingly being developed in order to be used by injured people to perform exercise and training. As these exercises do not need wide range movements, some parallel robots with lower mobility architecture can be an ideal solution for this purpose. This paper presents the design of a new four degree-of-freedom (DOF) parallel robot for knee rehabilitation. The required four DOFs are two translations in a vertical plane and two rotations, one of them around an axis perpendicular to the vertical plane and the other one with respect to a vector normal to the instantaneous orientation of the mobile platform. These four DOFs are reached by means of two RPRR limbs and two UPS limbs linked to an articulated mobile platform with an internal DOF. Kinematics of the new mechanism are solved and the direct Jacobian is calculated. A singularity analysis is carried out and the gained DOFs of the direct singularities are calculated. Some of the singularities can be avoided by selecting suitable values of the geometric parameters of the robot. Moreover, among the found singularities, one of them can be used in order to fold up the mechanism for its transportation. It is concluded that the proposed mechanism reaches the desired output movements in order to carry out rehabilitation maneuvers in a singularity-free portion of its workspace.

Novel Reconfigurable Spherical Parallel Mechanisms with a Circular Rail

“…To see this in detail, suppose we use the SPS chain, where point N does not coincide with F, and fix its drive. The moving plate becomes constrained by two-dimensional constraint space (2) and wrench (11), which we can treat as a constraint wrench. Point F becomes fixed in space because a vector part of wrench (11) has a nonzero projection on the vertical axis.…”

“…The moving plate becomes constrained by two-dimensional constraint space (2) and wrench (11), which we can treat as a constraint wrench. Point F becomes fixed in space because a vector part of wrench (11) has a nonzero projection on the vertical axis. This wrench does not depend on (2), so we can find three linearly independent twists, 𝛏𝛏 1 ′ , 𝛏𝛏 2 ′ , and 𝛏𝛏 3 ′ , reciprocal to (2) and ( 11) that define plate DOFs.…”

“…The mechanism includes hip-knee and ankle modules, which allow it to perform hip flexion/extension, knee flexion, plantar flexion/dorsiflexion, and ankle eversion/inversion. Paper [11] presented a 4-DOF 2RPRR-2UPS mechanism for knee rehabilitation; its output link can perform planar motion and additional rotation. Work [12] considered a 9-DOF hybrid (parallel-serial) mechanism for foot rehabilitation.…”

Error identification and compensation of 1T2R parallel power head based on trajectory optimization and principal component analysis

“…Menq et al (1989) and Menq and Borm (1991) first proposed the concept of an observation index to evaluate and optimize the error measurement configuration of an open-loop planar mechanism and PUMA robot. Subsequently, based on the singular value of the error transfer matrix, scholars have proposed five observation indicators: O 1 , O 2 , O 3 , O 4 and O 5 (Menq and Borm, 1991; Nahvi and Hollerbach, 1996; Wang et al , 2017; Zhang et al , 2019; Sun and Hollerbach, 2008), and their effectiveness has also been widely investigated. The O 1 observation index is the most effective when the variation of the minimum identification parameters is taken as the objective (Menq et al , 1989; Menq and Borm, 1991; Qiao et al , 2021; Daney et al , 2005).…”

“…The O 1 observation index is the most effective when the variation of the minimum identification parameters is taken as the objective (Menq et al , 1989; Menq and Borm, 1991; Qiao et al , 2021; Daney et al , 2005). When the change in the minimum endpoint error is taken as the target, the O 3 observation index is the most reasonable (Wang et al , 2017; Zhou et al , 2014). When the mean value of the calibrated mechanism position error is taken as the reference standard, the geometric error identification effect of the measured position and attitude under the O 2 observation index is better (Joubair et al , 2013; Khalil and Gautier, 1991).…”