## 1 Introduction  
As people age, the generation of vertical support forces during walking declines [1, 2, 3, 4, 5]. Vertical support forces are the forces acting on the body in the vertical direction, playing a crucial role in maintaining stability and supporting body weight during weight-bearing activities. The magnitude of vertical ground reaction forces (VGRF) is influenced by factors such as muscle strength, gait mechanics, and overall body mass. In older adults, a decline in VGRF is often associated with lower-limb muscle weaknesses and slower walking speed in older adults [6, 7] and may increase the risk of falls. VGRF during the stance phase relies on the combined output of ankle, knee, and hip extension torques [8]. Compared to younger adults, older adults show a redistribution of joint torques, relying more on hip extensors and less on ankle plantar flexors and knee extensors [1, 5, 9, 10, 11, 12, 13, 14, 15, 16]. This distal-to-proximal joint torque redistribution appears to be consistent regardless of walking speed, level of physical activity, or gender [10, 17] and is associated with an increased energy cost of walking in the elderly population [18].  
With aging, there is a well-documented reduction in knee extensor function [19; 20; 21; 22], which has been associated with slower walking speed and shorter step length in healthy older adults [23]. After heel strike, knee joint flexion provides shock absorption during the loading response phase when the body weight is transferred onto the leading limb. At this moment, knee extensor muscles contract eccentrically to control the knee flexion motion [24; 25]. Older adults show a moderate degree of atrophy in their quadriceps muscles [20], which may compromise knee extensor function during gait. The higher reliance on hip extensor torque in older adults suggests a potential compensatory mechanism for knee extensor muscle weakness [15; 26]. Consequently, task-oriented walking training targeting both vertical support forces and knee extensor torque in older adults is needed.  
Previous research has shown that real-time force biofeedback effectively increases VGRF peak and knee extension torque in individuals with knee pathologies. For instance, in post-ACL reconstruction patients, a 5% increase in the first peak of VGRF led to a 13.22% increase in knee extension torque [27; 28]. However, no studies have specifically investigated the effect of VGRF biofeedback on older adults, who typically exhibit lower VGRF during walking and rely more on hip extensors due to knee extensor weakness. This study addresses this gap by investigating whether VGRF biofeedback can enhance knee extension torque and reduce compensatory hip torque, thereby mitigating age-related distal-to-proximal joint torque redistribution. Therefore, the purpose of this study was to determine the effect of VGRF real-time biofeedback on knee and hip joint kinetics, kinematics, and extensor muscle activities in older adults. We hypothesized that older adults would show increased peak VGRF, peak knee extension torque, peak knee flexion angle, knee flexion excursion, and knee extensor muscle activities during biofeedback, immediately following the biofeedback, and after a 5 min break, compared to baseline walking. We further hypothesize that with increasing VGRF, older adults will show greater knee extension torque contribution relative to hip extension torque during biofeedback and recall trials compared to baseline walking.