The standard for negligence for a careless or reckless action as opposed to a premises situation is to evaluate what the owner knew or should have known to determine whether their actions were unreasonable under the circumstances. In a gym, that includes prior knowledge of the equipment.
Understanding the equipment could help gym staff identify an equipment error and prevent potential injury to visitors. Failure to take necessary action in this instance could be evidence of negligence.
In most cases, the gym owner can be held responsible for injuries that occur on their premises if they knew or should have known of a particular problem or dangerous situation and failed to warn somebody about it. However, sometimes the fault can fall on intermediaries.
Many gyms allow private trainers or allow people to come in and use their equipment to help others train. Trainers can be held responsible if they misused a piece of equipment, misguide their clients on how to use a piece of equipment, or fail to ensure that equipment is being used in a proper manner.
Manufacturers could also be potentially liable if there was a design issue that the gym owner would not be aware of. Furthermore, if the warning signs were placed by the manufacturer of the equipment and fails to adequately warn a user of the dangers, injured parties might be able to maintain a case against the manufacturer for failing to warn of the known hazard.
These situations need to be evaluated carefully as there may be multiple people that are responsible. A local attorney could determine whether the gym owner, personal trainer, or equipment manufacturer are responsible for an accident.