**1. Introduction**

In our daily lives, we repeatedly travel to and from our destinations to accomplish our goals, often choosing walking as our means of transportation. However, disabled or elderly people who cannot walk safely may choose a wheelchair as their means of transportation [1]. When we walk or sit in a wheelchair, we need to perform a standing movement (sitting to standing (STS)). However, disabled and elderly people may not be able to perform the STS movement and may not be able to continue to live independently. Therefore, sometimes, the goal of rehabilitation in hospitals and nursing homes is to ensure that the patient achieves the STS ability [2]. Post-hip-fracture and post-stroke patients targeted for rehabilitation have been reported to have asymmetric STS movements due to muscle weakness and impaired sensory integration in the lower limbs [3,4]. Pao-Tsai et al. reported that post-stroke patients who had experienced falls had greater asymmetry in the weight distribution to the lower limbs during the STS movement [5]; the asymmetry of the STS movements is shaped by the associated muscle forces and joint moments. Previous studies examining weight bearing in the lower limbs of post-stroke patients have reported that patients often shift their center of gravity to the nonparalyzed lower limb [6]. However, mechanical asymmetry of the lower limb during the STS movement may reduce safety when the person is performing an even more advanced and dynamic gait [7]. Ryoichiro et al. reported an STS rehabilitation system that improves the functional asymmetry of the lower limb caused by disease [8]. These previous studies indicate that it is important for rehabilitation to improve the muscle strength, movement, and asymmetric STS movement of the asymmetric lower limb.

**Citation:** Nakamura, K.; Saga, N. A Symmetry Evaluation Method, Using Elevation Angle, for Lower Limb Movement Patterns during Sitting-to-Standing. *Appl. Sci.* **2022**, *12*, 9454. https://doi.org/10.3390/ app12199454

Academic Editors: Luis Gracia and Carlos Perez-Vidal

Received: 17 August 2022 Accepted: 17 September 2022 Published: 21 September 2022

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Department of Engineering, Kwansei Gakuin University, 1 Gakuenuegahara, Sanda 669-1330, Hyogo, Japan

In previous studies on STS symmetry, lower limb joint torque and floor reaction force were selected as mechanical parameters and joint angle as a kinematic parameter, parameters that can be observed in measurement experiments [9–11]. These parameters are observed as a result of the human central nervous system controlling the muscles (the locomotion organs). In Japan today, cerebrovascular disorders are the leading cause of the need for long-term care [12] and normalization of muscle activity patterns and centerof-gravity trajectories during movement through rehabilitation-incorporating robots is becoming the treatment of choice [13]. In other words, rehabilitation of the central nervous system, which controls muscle activity temporally and spatially, rather than rehabilitation to increase motor muscle mass and the force exerted by the muscles, is attracting attention. Ningjia et al. analyzed muscle synergy during the STS movement in stroke patients [14]. However, this report mentions asymmetry based on the analysis of muscle synergy but does not propose a quantitative method for evaluating symmetry and asymmetry. Wendy et al. proposed a symmetry index in their report on STS symmetry evaluation [9]. This method measures the angles of the right and left (R–L) lower limb joints during the STS movement and calculates the ratio of the angles as a symmetry index. Michalina et al. selected ankle, knee, and hip joint angles, joint torque, and floor reaction force as symmetry indices [11]. These previous studies converted the observed information into a single value as an index of symmetry and cannot represent the motion patterns during the STS movement.

The planar law of gait (PLG) is a well-known evaluation method that allows us to observe the coordination patterns of the neurophysiological body movement based on changes in joint angles observed over time during movement [15,16]. The PLG involves the three-dimensional plotting of the elevation angles (EAs) of three segments (thigh, shin, and foot) during walking. Gianluca et al. used the PLG of the L–R lower limbs to present the symmetry of the walking motion as visual information [17]. They evaluated the symmetry; if the PLG could be applied to the STS movement and the STS movement symmetry could be quantitatively evaluated, it would be possible to geometrically evaluate the symmetry of the control by the central nervous system during the STS movement. However, there are different factors involved in the STS movement and gait. In the gait, the EAs of three segments (thigh, shank, and foot) are observed, but in the STS movement the EA of the foot is always constant because the foot is restrained above the floor and only changes in the EAs of two segments (thigh and shank) are observed. Therefore, the observed changes in the EAs of the two body segments in the STS movement cannot be plotted on 3D coordinates as in the gait. Furthermore, since the STS movement is not a periodic motion similar to a gait, the PLG cannot be directly adapted to the STS movement.
